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Structural equation modeling

Structural equation modeling (SEM) is a diverse set of methods used by scientists doing both observational and experimental research. SEM is used mostly in the social and behavioral sciences but it is also used in epidemiology, business, and other fields. A definition of SEM is difficult without reference to technical language, but a good starting place is the name itself.

SEM involves a model representing how various aspects of some phenomenon are thought to causally connect to one another. Structural equation models often contain postulated causal connections among some latent variables (variables thought to exist but which can't be directly observed). Additional causal connections link those latent variables to observed variables whose values appear in a data set. The causal connections are represented using equations but the postulated structuring can also be presented using diagrams containing arrows as in Figures 1 and 2. The causal structures imply that specific patterns should appear among the values of the observed variables. This makes it possible to use the connections between the observed variables' values to estimate the magnitudes of the postulated effects, and to test whether or not the observed data are consistent with the requirements of the hypothesized causal structures.

The boundary between what is and is not a structural equation model is not always clear but SE models often contain postulated causal connections among a set of latent variables (variables thought to exist but which can't be directly observed, like an attitude, intelligence or mental illness) and causal connections linking the postulated latent variables to variables that can be observed and whose values are available in some data set. Variations among the styles of latent causal connections, variations among the observed variables measuring the latent variables, and variations in the statistical estimation strategies result in the SEM toolkit including confirmatory factor analysis, confirmatory composite analysis, path analysis, multi-group modeling, longitudinal modeling, partial least squares path modeling, latent growth modeling and hierarchical or multilevel modeling.

SEM researchers use computer programs to estimate the strength and sign of the coefficients corresponding to the modeled structural connections, for example the numbers connected to the arrows in Figure 1. Because a postulated model such as Figure 1 may not correspond to the worldly forces controlling the observed data measurements, the programs also provide model tests and diagnostic clues suggesting which indicators, or which model components, might introduce inconsistency between the model and observed data. Criticisms of SEM methods hint at: disregard of available model tests, problems in the model's specification, a tendency to accept models without considering external validity, and potential philosophical biases.

A great advantage of SEM is that all of these measurements and tests occur simultaneously in one statistical estimation procedure, where all the model coefficients are calculated using all information from the observed variables. This means the estimates are more accurate than if a researcher were to calculate each part of the model separately.

History
Structural equation modeling (SEM) began differentiating itself from correlation and regression when Sewall Wright provided explicit causal interpretations for a set of regression-style equations based on a solid understanding of the physical and physiological mechanisms producing direct and indirect effects among his observed variables. The equations were estimated like ordinary regression equations but the substantive context for the measured variables permitted clear causal, not merely predictive, understandings. O. D. Duncan introduced SEM to the social sciences in his 1975 book and SEM blossomed in the late 1970's and 1980's when increasing computing power permitted practical model estimation. In 1987 Hayduk provided the first book-length introduction to structural equation modeling with latent variables, and this was soon followed by Bollen's popular text (1989).

Different yet mathematically related modeling approaches developed in psychology, sociology, and economics. Early Cowles Commission work on simultaneous equations estimation centered on Koopman and Hood's (1953) algorithms from transport economics and optimal routing, with maximum likelihood estimation, and closed form algebraic calculations, as iterative solution search techniques were limited in the days before computers. The convergence of two of these developmental streams (factor analysis from psychology, and path analysis from sociology via Duncan) produced the current core of SEM. One of several programs Karl Jöreskog developed at Educational Testing Services, LISREL  embedded latent variables (which psychologists knew as the latent factors from factor analysis) within path-analysis-style equations (which sociologists inherited from Wright and Duncan). The factor-structured portion of the model incorporated measurement errors which permitted measurement-error-adjustment, though not necessarily error-free estimation, of effects connecting different postulated latent variables.

Traces of the historical convergence of the factor analytic and path analytic traditions persist as the distinction between the measurement and structural portions of models; and as continuing disagreements over model testing, and whether measurement should precede or accompany structural estimates. Viewing factor analysis as a data-reduction technique deemphasizes testing, which contrasts with path analytic appreciation for testing postulated causal connections – where the test result might signal model misspecification. The friction between factor analytic and path analytic traditions continue to surface in the literature.

Wright's path analysis influenced Hermann Wold, Wold's student Karl Jöreskog, and Jöreskog's student Claes Fornell, but SEM never gained a large following among U.S. econometricians, possibly due to fundamental differences in modeling objectives and typical data structures. The prolonged separation of SEM's economic branch led to procedural and terminological differences, though deep mathematical and statistical connections remain. The economic version of SEM can be seen in SEMNET discussions of endogeneity, and in the heat produced as Judea Pearl's approach to causality via directed acyclic graphs (DAG's) rubs against economic approaches to modeling. Discussions comparing and contrasting various SEM approaches are available but disciplinary differences in data structures and the concerns motivating economic models make reunion unlikely. Pearl extended SEM from linear to nonparametric models, and proposed causal and counterfactual interpretations of the equations. Nonparametric SEMs permit estimating total, direct and indirect effects without making any commitment to linearity of effects or assumptions about the distributions of the error terms.

SEM analyses are popular in the social sciences because computer programs make it possible to estimate complicated causal structures, but the complexity of the models introduces substantial variability in the quality of the results. Some, but not all, results are obtained without the "inconvenience" of understanding experimental design, statistical control, the consequences of sample size, and other features contributing to good research design.

General steps and considerations
The following considerations apply to the construction and assessment of many structural equation models.

Model specification
Building or specifying a model requires attending to:
 * the set of variables to be employed,
 * what is known about the variables,
 * what is presumed or hypothesized about the variables' causal connections and disconnections,
 * what the researcher seeks to learn from the modeling,
 * and the cases for which values of the variables will be available (kids? workers? companies? countries? cells? accidents? cults?).

Structural equation models attempt to mirror the worldly forces operative for causally homogeneous cases – namely cases enmeshed in the same worldly causal structures but whose values on the causes differ and who therefore possess different values on the outcome variables. Causal homogeneity can be facilitated by case selection, or by segregating cases in a multi-group model. A model's specification is not complete until the researcher specifies:
 * which effects and/or correlations/covariances are to be included and estimated,
 * which effects and other coefficients are forbidden or presumed unnecessary,
 * and which coefficients will be given fixed/unchanging values (e.g. to provide measurement scales for latent variables as in Figure 2).

The latent level of a model is composed of endogenous and exogenous variables. The endogenous latent variables are the true-score variables postulated as receiving effects from at least one other modeled variable. Each endogenous variable is modeled as the dependent variable in a regression-style equation. The exogenous latent variables are background variables postulated as causing one or more of the endogenous variables and are modeled like the predictor variables in regression-style equations. Causal connections among the exogenous variables are not explicitly modeled but are usually acknowledged by modeling the exogenous variables as freely correlating with one another. The model may include intervening variables – variables receiving effects from some variables but also sending effects to other variables. As in regression, each endogenous variable is assigned a residual or error variable encapsulating the effects of unavailable and usually unknown causes. Each latent variable, whether exogenous or endogenous, is thought of as containing the cases' true-scores on that variable, and these true-scores causally contribute valid/genuine variations into one or more of the observed/reported indicator variables.

The LISREL program assigned Greek names to the elements in a set of matrices to keep track of the various model components. These names became relatively standard notation, though the notation has been extended and altered to accommodate a variety of statistical considerations. Texts and programs "simplifying" model specification via diagrams or by using equations permitting user-selected variable names, re-convert the user's model into some standard matrix-algebra form in the background. The "simplifications" are achieved by implicitly introducing default program "assumptions" about model features with which users supposedly need not concern themselves. Unfortunately, these default assumptions easily obscure model components that leave unrecognized issues lurking within the model's structure, and underlying matrices. Two main components of models are distinguished in SEM: the structural model showing potential causal dependencies between endogenous and exogenous latent variables, and the measurement model showing the causal connections between the latent variables and the indicators. Exploratory and confirmatory factor analysis models, for example, focus on the causal measurement connections, while path models more closely correspond to SEMs latent structural connections.

Modelers specify each coefficient in a model as being free to be estimated, or fixed at some value. The free coefficients may be postulated effects the researcher wishes to test, background correlations among the exogenous variables, or the variances of the residual or error variables providing additional variations in the endogenous latent variables. The fixed coefficients may be values like the 1.0 values in Figure 2 that provide a scales for the latent variables, or values of 0.0 which assert causal disconnections such as the assertion of no-direct-effects (no arrows) pointing from Academic Achievement to any of the four scales in Figure 1. SEM programs provide estimates and tests of the free coefficients, while the fixed coefficients contribute importantly to testing the overall model structure. Various kinds of constraints between coefficients can also be used. The model specification depends on what is known from the literature, the researcher's experience with the modeled indicator variables, and the features being investigated by using the specific model structure.

There is a limit to how many coefficients can be estimated in a model. If there are fewer data points than the number of estimated coefficients, the resulting model is said to be "unidentified" and no coefficient estimates can be obtained. Reciprocal effect, and other causal loops, may also interfere with estimation.

Estimation of free model coefficients
Model coefficients fixed at zero, 1.0, or other values, do not require estimation because they already have specified values. Estimated values for free model coefficients are obtained by maximizing fit to, or minimizing difference from, the data relative to what the data's features would be if the free model coefficients took on the estimated values. The model's implications for what the data should look like for a specific set of coefficient values depends on: a) the coefficients' locations in the model (e.g. which variables are connected/disconnected), b) the nature of the connections between the variables (covariances or effects; with effects often assumed to be linear), c) the nature of the error or residual variables (often assumed to be independent of, or causally-disconnected from, many variables), and d) the measurement scales appropriate for the variables (interval level measurement is often assumed).

A stronger effect connecting two latent variables implies the indicators of those latents should be more strongly correlated. Hence, a reasonable estimate of a latent's effect will be whatever value best matches the correlations between the indicators of the corresponding latent variables – namely the estimate-value maximizing the match with the data, or minimizing the differences from the data. With maximum likelihood estimation, the numerical values of all the free model coefficients are individually adjusted (progressively increased or decreased from initial start values) until they maximize the likelihood of observing the sample data – whether the data are the variables' covariances/correlations, or the cases' actual values on the indicator variables. Ordinary least squares estimates are the coefficient values that minimize the squared differences between the data and what the data would look like if the model was correctly specified, namely if all the model's estimated features correspond to real worldly features.

The appropriate statistical feature to maximize or minimize to obtain estimates depends on the variables' levels of measurement (estimation is generally easier with interval level measurements than with nominal or ordinal measures), and where a specific variable appears in the model (e.g. endogenous dichotomous variables create more estimation difficulties than exogenous dichotomous variables). Most SEM programs provide several options for what is to be maximized or minimized to obtain estimates the model's coefficients. The choices often include maximum likelihood estimation (MLE), full information maximum likelihood (FIML), ordinary least squares (OLS), weighted least squares (WLS), diagonally weighted least squares (DWLS), and two stage least squares.

One common problem is that a coefficient's estimated value may be underidentified because it is insufficiently constrained by the model and data. No unique best-estimate exists unless the model and data together sufficiently constrain or restrict a coefficient's value. For example, the magnitude of a single data correlation between two variables is insufficient to provide estimates of a reciprocal pair of modeled effects between those variables. The correlation might be accounted for by one of the reciprocal effects being stronger than the other effect, or the other effect being stronger than the one, or by effects of equal magnitude. Underidentified effect estimates can be rendered identified by introducing additional model and/or data constraints. For example, reciprocal effects can be rendered identified by constraining one effect estimate to be double, triple, or equivalent to, the other effect estimate, but the resultant estimates will only be trustworthy if the additional model constraint corresponds to the world's structure. Data on a third variable that directly causes only one of a pair of reciprocally causally connected variables can also assist identification. Constraining a third variable to not directly cause one of the reciprocally-causal variables breaks the symmetry otherwise plaguing the reciprocal effect estimates because that third variable must be more strongly correlated with the variable it causes directly than with the variable at the "other" end of the reciprocal which it impacts only indirectly. Notice that this again presumes the properness of the model's causal specification – namely that there really is a direct effect leading from the third variable to the variable at this end of the reciprocal effects and no direct effect on the variable at the "other end" of the reciprocally connected pair of variables. Theoretical demands for null/zero effects provide helpful constraints assisting estimation, though theories often fail to clearly report which effects are allegedly nonexistent.

Model assessment
Model assessment depends on the theory, the data, the model, and the estimation strategy. Hence model assessments consider:
 * whether the data contain reasonable measurements of appropriate variables,
 * whether the modeled case are causally homogeneous, (It makes no sense to estimate one model if the data cases reflect two or more different causal networks.)
 * whether the model appropriately represents the theory or features of interest, (Models are unpersuasive if they omit features required by a theory, or contain coefficients inconsistent with that theory.)
 * whether the estimates are statistically justifiable, (Substantive assessments may be devastated: by violating assumptions, by using an inappropriate estimator, and/or by encountering non-convergence of iterative estimators.)
 * the substantive reasonableness of the estimates, (Negative variances, and correlations exceeding 1.0 or -1.0, are impossible. Statistically possible estimates that are inconsistent with theory may also challenge theory, and our understanding.)
 * the remaining consistency, or inconsistency, between the model and data. (The estimation process minimizes the differences between the model and data but important and informative differences may remain.)

Research claiming to test or "investigate" a theory requires attending to beyond-chance model-data inconsistency. Estimation adjusts the model's free coefficients to provide the best possible fit to the data. The output from SEM programs includes a matrix reporting the relationships among the observed variables that would be observed if the estimated model effects actually controlled the observed variables' values. The "fit" of a model reports match or mismatch between the model-implied relationships (often covariances) and the corresponding observed relationships among the variables. Large and significant differences between the data and the model's implications signal problems. The probability accompanying a $χ^{2}$ (chi-squared) test is the probability that the data could arise by random sampling variations if the estimated model constituted the real underlying population forces. A small $χ^{2}$ probability reports it would be unlikely for the current data to have arisen if the modeled structure constituted the real population causal forces – with the remaining differences attributed to random sampling variations.

If a model remains inconsistent with the data despite selecting optimal coefficient estimates, an honest research response reports and attends to this evidence (often a significant model $χ^{2}$ test). Beyond-chance model-data inconsistency challenges both the coefficient estimates and the model's capacity for adjudicating the model's structure, irrespective of whether the inconsistency originates in problematic data, inappropriate statistical estimation, or incorrect model specification. Coefficient estimates in data-inconsistent ("failing") models are interpretable, as reports of how the world would appear to someone believing a model that conflicts with the available data. The estimates in data-inconsistent models do not necessarily become "obviously wrong" by becoming statistically strange, or wrongly signed according to theory. The estimates may even closely match a theory's requirements but the remaining data inconsistency renders the match between the estimates and theory unable to provide succor. Failing models remain interpretable, but only as interpretations that conflict with available evidence.

Replication is unlikely to detect misspecified models which inappropriately-fit the data. If the replicate data is within random variations of the original data, the same incorrect coefficient placements that provided inappropriate-fit to the original data will likely also inappropriately-fit the replicate data. Replication helps detect issues such as data mistakes (made by different research groups), but is especially weak at detecting misspecifications after exploratory model modification – as when confirmatory factor analysis (CFA) is applied to a random second-half of data following exploratory factor analysis (EFA) of first-half data.

A modification index is an estimate of how much a model's fit to the data would "improve" (but not necessarily how much the model's structure would improve) if a specific currently-fixed model coefficient were freed for estimation. Researchers confronting data-inconsistent models can easily free coefficients the modification indices report as likely to produce substantial improvements in fit. This simultaneously introduces a substantial risk of moving from a causally-wrong-and-failing model to a causally-wrong-but-fitting model because improved data-fit does not provide assurance that the freed coefficients are substantively reasonable or world matching. The original model may contain causal misspecifications such as incorrectly directed effects, or incorrect assumptions about unavailable variables, and such problems cannot be corrected by adding coefficients to the current model. Consequently, such models remain misspecified despite the closer fit provided by additional coefficients. Fitting yet worldly-inconsistent models are especially likely to arise if a researcher committed to a particular model (for example a factor model having a desired number of factors) gets an initially-failing model to fit by inserting measurement error covariances "suggested" by modification indices. MacCallum (1986) demonstrated that "even under favorable conditions, models arising from specification serchers must be viewed with caution." Model misspecification may sometimes be corrected by insertion of coefficients suggested by the modification indices, but many more corrective possibilities are raised by employing a few indicators of similar-yet-importantly-different latent variables.

"Accepting" failing models as "close enough" is also not a reasonable alternative. A cautionary instance was provided by Browne, MacCallum, Kim, Anderson, and Glaser who addressed the mathematics behind why the $χ^{2}$ test can have (though it does not always have) considerable power to detect model misspecification. The probability accompanying a $χ^{2}$ test is the probability that the data could arise by random sampling variations if the current model, with its optimal estimates, constituted the real underlying population forces. A small $χ^{2}$ probability reports it would be unlikely for the current data to have arisen if the current model structure constituted the real population causal forces – with the remaining differences attributed to random sampling variations. Browne, McCallum, Kim, Andersen, and Glaser presented a factor model they viewed as acceptable despite the model being significantly inconsistent with their data according to $χ^{2}$. The fallaciousness of their claim that close-fit should be treated as good enough was demonstrated by Hayduk, Pazkerka-Robinson, Cummings, Levers and Beres who demonstrated a fitting model for Browne, et al.'s own data by incorporating an experimental feature Browne, et al. overlooked. The fault was not in the math of the indices or in the over-sensitivity of $χ^{2}$ testing. The fault was in Browne, MacCallum, and the other authors forgetting, neglecting, or overlooking, that the amount of ill fit cannot be trusted to correspond to the nature, location, or seriousness of problems in a model's specification.

Many researchers tried to justify switching to fit-indices, rather than testing their models, by claiming that $χ^{2}$ increases (and hence $χ^{2}$ probability decreases) with increasing sample size (N). There are two mistakes in discounting $χ^{2}$ on this basis. First, for proper models, $χ^{2}$ does not increase with increasing N, so if $χ^{2}$ increases with N that itself is a sign that something is detectably problematic. And second, for models that are detectably misspecified, $χ^{2}$ increase with N provides the good-news of increasing statistical power to detect model misspecification (namely power to detect Type II error). Some kinds of important misspecifications cannot be detected by $χ^{2}$, so any amount of ill fit beyond what might be reasonably produced by random variations warrants report and consideration. The $χ^{2}$ model test, possibly adjusted, is the strongest available structural equation model test.

Numerous fit indices quantify how closely a model fits the data but all fit indices suffer from the logical difficulty that the size or amount of ill fit is not trustably coordinated with the severity or nature of the issues producing the data inconsistency. Models with different causal structures which fit the data identically well, have been called equivalent models. Such models are data-fit-equivalent though not causally equivalent, so at least one of the so-called equivalent models must be inconsistent with the world's structure. If there is a perfect 1.0 correlation between X and Y and we model this as X causes Y, there will be perfect fit and zero residual error. But the model may not match the world because Y may actually cause X, or both X and Y may be responding to a common cause Z, or the world may contain a mixture of these effects (e.g. like a common cause plus an effect of Y on X), or other causal structures. The perfect fit does not tell us the model's structure corresponds to the world's structure, and this in turn implies that getting closer to perfect fit does not necessarily correspond to getting closer to the world's structure – maybe it does, maybe it doesn't. This makes it incorrect for a researcher to claim that even perfect model fit implies the model is correctly causally specified. For even moderately complex models, precisely equivalently-fitting models are rare. Models almost-fitting the data, according to any index, unavoidably introduce additional potentially-important yet unknown model misspecifications. These models constitute a greater research impediment.

This logical weakness renders all fit indices "unhelpful" whenever a structural equation model is significantly inconsistent with the data, but several forces continue to propagate fit-index use. For example, Dag Sorbom reported that when someone asked Karl Joreskog, the developer of the first structural equation modeling program, "Why have you then added GFI?" to your LISREL program, Joreskog replied "Well, users threaten us saying they would stop using LISREL if it always produces such large chi-squares. So we had to invent something to make people happy. GFI serves that purpose." The $χ^{2}$ evidence of model-data inconsistency was too statistically solid to be dislodged or discarded, but people could at least be provided a way to distract from the "disturbing" evidence. Career-profits can still be accrued by developing additional indices, reporting investigations of index behavior, and publishing models intentionally burying evidence of model-data inconsistency under an MDI (a mound of distracting indices). There seems no general justification for why a researcher should "accept" a causally wrong model, rather than attempting to correct detected misspecifications. And some portions of the literature seems not to have noticed that "accepting a model" (on the basis of "satisfying" an index value) suffers from an intensified version of the criticism applied to "acceptance" of a null-hypothesis. Introductory statistics texts usually recommend replacing the term "accept" with "failed to reject the null hypothesis" to acknowledge the possibility of Type II error. A Type III error arises from "accepting" a model hypothesis when the current data are sufficient to reject the model.

Whether or not researchers are committed to seeking the world’s structure is a fundamental concern. Displacing test evidence of model-data inconsistency by hiding it behind index claims of acceptable-fit, introduces the discipline-wide cost of diverting attention away from whatever the discipline might have done to attain a structurally-improved understanding of the discipline’s substance. The discipline ends up paying a real costs for index-based displacement of evidence of model misspecification. The frictions created by disagreements over the necessity of correcting model misspecifications will likely increase with increasing use of non-factor-structured models, and with use of fewer, more-precise, indicators of similar yet importantly-different latent variables.

The considerations relevant to using fit indices include checking:
 * 1)  whether data concerns have been addressed (to ensure data mistakes are not driving model-data inconsistency);
 * 2)  whether criterion values for the index have been investigated for models structured like the researcher's model (e.g. index criterion based on factor structured models are only appropriate if the researcher's model actually is factor structured);
 * 3)  whether the kinds of potential misspecifications in the current model correspond to the kinds of misspecifications on which the index criterion are based (e.g. criteria based on simulation of omitted factor loadings may not be appropriate for misspecification resulting from failure to include appropriate control variables);
 * 4)  whether the researcher knowingly agrees to disregard evidence pointing to the kinds of misspecifications on which the index criteria were based. (If the index criterion is based on simulating a missing factor loading or two, using that criterion acknowledges the researcher's willingness to accept a model missing a factor loading or two.);
 * 5)  whether the latest, not outdated, index criteria are being used (because the criteria for some indices tightened over time);
 * 6)  whether satisfying criterion values on pairs of indices are required (e.g. Hu and Bentler report that some common indices function inappropriately unless they are assessed together.);
 * 7)  whether a model test is, or is not, available. (A $χ^{2}$ value, degrees of freedom, and probability will be available for models reporting indices based on $χ^{2}$.)
 * 8) and whether the researcher has considered both alpha (Type I) and beta (Type II) errors in making their index-based decisions (E.g. if the model is significantly data-inconsistent, the "tolerable" amount of inconsistency is likely to differ in the context of medical, business, social and psychological contexts.).

Some of the more commonly used fit statistics include
 * Chi-square
 * A fundamental test of fit used in the calculation of many other fit measures. It is a function of the discrepancy between the observed covariance matrix and the model-implied covariance matrix. Chi-square increases with sample size only if the model is detectably misspecified.
 * Akaike information criterion (AIC)
 * An index of relative model fit: The preferred model is the one with the lowest AIC value.
 * $$\mathit{AIC} = 2k - 2\ln(L)\,$$
 * where k is the number of parameters in the statistical model, and L is the maximized value of the likelihood of the model.
 * Root Mean Square Error of Approximation (RMSEA)
 * Fit index where a value of zero indicates the best fit. Guidelines for determining a "close fit" using RMSEA are highly contested.
 * Standardized Root Mean Squared Residual (SRMR)
 * The SRMR is a popular absolute fit indicator. Hu and Bentler (1999) suggested .08 or smaller as a guideline for good fit.
 * Comparative Fit Index (CFI)
 * In examining baseline comparisons, the CFI depends in large part on the average size of the correlations in the data. If the average correlation between variables is not high, then the CFI will not be very high. A CFI value of .95 or higher is desirable.

The following table provides references documenting these, and other, features for some common indices: the RMSEA (Root Mean Square Error of Approximation), SRMR (Standardized Root Mean Squared Residual), CFI (Confirmatory Fit Index), and the TLI (the Tucker-Lewis Index). Additional indices such as the AIC (Akaike Information Criterion) can be found in most SEM introductions. For each measure of fit, a decision as to what represents a good-enough fit between the model and the data reflects the researcher's modeling objective (perhaps challenging someone else's model, or improving measurement); whether or not the model is to be claimed as having been "tested"; and whether the researcher is comfortable "disregarding" evidence of the index-documented degree of ill fit.

Sample size, power, and estimation
Researchers agree samples should be large enough to provide stable coefficient estimates and reasonable testing power but there is no general consensus regarding specific required sample sizes, or even how to determine appropriate sample sizes. Recommendations have been based on the number of coefficients to be estimated, the number of modeled variables, and Monte Carlo simulations addressing specific model coefficients. Sample size recommendations based on the ratio of the number of indicators to latents are factor oriented and do not apply to models employing single indicators having fixed nonzero measurement error variances. Overall, for moderate sized models without statistically difficult-to-estimate coefficients, the required sample sizes (N’s) seem roughly comparable to the N’s required for a regression employing all the indicators.

The larger the sample size, the greater the likelihood of including cases that are not causally homogeneous. Consequently, increasing N to improve the likelihood of being able to report a desired coefficient as statistically significant, simultaneously increases the risk of model misspecification, and the power to detect the misspecification. Researchers seeking to learn from their modeling (including potentially learning their model requires adjustment or replacement) will strive for as large a sample size as permitted by funding and by their assessment of likely population-based causal heterogeneity/homogeneity. If the available N is huge, modeling sub-sets of cases can control for variables that might otherwise disrupt causal homogeneity. Researchers fearing they might have to report their model’s deficiencies are torn between wanting a larger N to provide sufficient power to detect structural coefficients of interest, while avoiding the power capable of signaling model-data inconsistency. The huge variation in model structures and data characteristics suggests adequate sample sizes might be usefully located by considering other researchers’ experiences (both good and bad) with models of comparable size and complexity that have been estimated with similar data.

Interpretation
Causal interpretations of SE models are the clearest and most understandable but those interpretations will be fallacious/wrong if the model’s structure does not correspond to the world’s causal structure. Consequently, interpretation should address the overall status and structure of the model, not merely the model’s estimated coefficients. Whether a model fits the data, and/or how a model came to fit the data, are paramount for interpretation. Data fit obtained by exploring, or by following successive modification indices, does not guarantee the model is wrong but raises serious doubts because these approaches are prone to incorrectly modeling data features. For example, exploring to see how many factors are required preempts finding the data are not factor structured, especially if the factor model has been “persuaded” to fit via inclusion of measurement error covariances. Data’s ability to speak against a postulated model is progressively eroded with each unwarranted inclusion of a “modification index suggested” effect or error covariance. It becomes exceedingly difficult to recover a proper model if the initial/base model contains several misspecifications.

Direct-effect estimates are interpreted in parallel to the interpretation of coefficients in regression equations but with causal commitment. Each unit increase in a causal variable’s value is viewed as producing a change of the estimated magnitude in the dependent variable’s value given control or adjustment for all the other operative/modeled causal mechanisms. Indirect effects are interpreted similarly, with the magnitude of a specific indirect effect equaling the product of the series of direct effects comprising that indirect effect. The units involved are the real scales of observed variables’ values, and the assigned scale values for latent variables. A specified/fixed 1.0 effect of a latent on a specific indicator coordinates that indicator’s scale with the latent variable’s scale. The presumption that the remainder of the model remains constant or unchanging may require discounting indirect effects that might, in the real world, be simultaneously prompted by a real unit increase. And the unit increase itself might be inconsistent with what is possible in the real world because there may be no known way to change the causal variable’s value. If a model adjusts for measurement errors, the adjustment permits interpreting latent-level effects as referring to variations in true scores.

SEM interpretations depart most radically from regression interpretations when a network of causal coefficients connects the latent variables because regressions do not contain estimates of indirect effects. SEM interpretations should convey the consequences of the patterns of indirect effects that carry effects from background variables through intervening variables to the downstream dependent variables. SEM interpretations encourage understanding how multiple worldly causal pathways can work in coordination, or independently, or even counteract one another. Direct effects may be counteracted (or reinforced) by indirect effects, or have their correlational implications counteracted (or reinforced) by the effects of common causes. The meaning and interpretation of specific estimates should be contextualized in the full model.

SE model interpretation should connect specific model causal segments to their variance and covariance implications. A single direct effect reports that the variance in the independent variable produces a specific amount of variation in the dependent variable’s values, but the causal details of precisely what makes this happens remains unspecified because a single effect coefficient does not contain sub-components available for integration into a structured story of how that effect arises. A more fine-grained SE model incorporating variables intervening between the cause and effect would be required to provide features constituting a story about how any one effect functions. Until such a model arrives each estimated direct effect retains a tinge of the unknown, thereby invoking the essence of a theory. A parallel essential unknownness would accompany each estimated coefficient in even the more fine-grained model, so the sense of fundamental mystery is never fully eradicated from SE models. Even if each modeled effect is unknown beyond the identity of the variables involved and the estimated magnitude of the effect, the structures linking multiple modeled effects provide opportunities to express how things function to coordinate the observed variables – thereby providing useful interpretation possibilities. For example, a common cause contributes to the covariance or correlation between two effected variables, because if the value of the cause goes up, the values of both effects should also go up (assuming positive effects) even if we do not know the full story underlying each cause. (A correlation is the covariance between two variables that have both been standardized to have variance 1.0). Another interpretive contribution might be made by expressing how two causal variables can both explain variance in a dependent variable, as well as how covariance between two such causes can increase or decrease explained variance in the dependent variable. That is, interpretation may involve explaining how a pattern of effects and covariances can contribute to decreasing a dependent variable’s variance. Understanding causal implications implicitly connects to understanding “controlling”, and potentially explaining why some variables, but not others, should be controlled. As models become more complex these fundamental components can combine in non-intuitive ways, such as explaining how there can be no correlation (zero covariance) between two variables despite the variables being connected by a direct non-zero causal effect.

The statistical insignificance of an effect estimate indicates the estimate could rather easily arise as a random sampling variation around a null/zero effect, so interpreting the estimate as a real effect becomes equivocal. As in regression, the proportion of each dependent variable’s variance explained by variations in the modeled causes are provided by R2, though the Blocked-Error R2 should be used if the dependent variable is involved in reciprocal or looped effects, or if it has an error variable correlated with any predictor’s error variable.

The caution appearing in the Model Assessment section warrants repeat. Interpretation should be possible whether a model is or is not consistent with the data. The estimates report how the world would appear to someone believing the model – even if that belief is unfounded because the model happens to be wrong. Interpretation should acknowledge that the model coefficients may or may not correspond to “parameters” – because the model’s coefficients may not have corresponding worldly structural features.

Adding new latent variables entering or exiting the original model at a few clear causal locations/variables contributes to detecting model misspecifications which could otherwise ruin coefficient interpretations. The correlations between the new latent’s indicators and all the original indicators contribute to testing the original model’s structure because the few new and focused effect coefficients must work in coordination with the model’s original direct and indirect effects to coordinate the new indicators with the original indicators. If the original model’s structure was problematic, the sparse new causal connections will be insufficient to coordinate the new indicators with the original indicators, thereby signaling the inappropriateness of the original model’s coefficients through model-data inconsistency. The correlational constraints grounded in null/zero effect coefficients, and coefficients assigned fixed nonzero values, contribute to both model testing and coefficient estimation, and hence deserve acknowledgment as the scaffolding supporting the estimates and their interpretation.

Interpretations become progressively more complex for models containing interactions, nonlinearities, multiple groups, multiple levels, and categorical variables. Effects touching causal loops, reciprocal effects, or correlated residuals also require slightly revised interpretations. Careful interpretation of both failing and fitting models can provide research advancement. To be dependable, the model should investigate academically informative causal structures, fit applicable data with understandable estimates, and not include vacuous coefficients. Dependable fitting models are rarer than failing models or models inappropriately bludgeoned into fitting, but appropriately-fitting models are possible.

The multiple ways of conceptualizing PLS models complicate interpretation of PLS models. Many of the above comments are applicable if a PLS modeler adopts a realist perspective by striving to ensure their modeled indicators combine in a way that matches some existing but unavailable latent variable. Non-causal PLS models, such as those focusing primarily on R2 or out-of-sample predictive power, change the interpretation criteria by diminishing concern for whether or not the model’s coefficients have worldly counterparts. The fundamental features differentiating the five PLS modeling perspectives discussed by Rigdon, Sarstedt and Ringle point to differences in PLS modelers’ objectives, and corresponding differences in model features warranting interpretation.

Caution should be taken when making claims of causality even when experiments or time-ordered investigations have been undertaken. The term causal model must be understood to mean "a model that conveys causal assumptions", not necessarily a model that produces validated causal conclusions—maybe it does maybe it does not. Collecting data at multiple time points and using an experimental or quasi-experimental design can help rule out certain rival hypotheses but even a randomized experiments cannot fully rule out threats to causal claims. No research design can fully guarantee causal structures.

Controversies and movements
Structural equation modeling is fraught with controversies. Researchers from the factor analytic tradition commonly attempt to reduce sets of multiple indicators to fewer, more manageable, scales or factor-scores for later use in path-structured models. This constitutes a stepwise process with the initial measurement step providing scales or factor-scores which are to be used later in a path-structured model. This stepwise approach seems obvious but actually confronts severe underlying deficiencies. The segmentation into steps interferes with thorough checking of whether the scales or factor-scores validly represent the indicators, and/or validly report on latent level effects. A structural equation model simultaneously incorporating both the measurement and latent-level structures not only checks whether the latent factors appropriately coordinates the indicators, it also checks whether that same latent simultaneously appropriately coordinates each latent’s indictors with the indicators of theorized causes and/or consequences of that latent. If a latent is unable to do both these styles of coordination, the validity of that latent is questioned, and a scale or factor-scores purporting to measure that latent is questioned. The disagreements swirled around respect for, or disrespect of, evidence challenging the validity of postulated latent factors. The simmering, sometimes boiling, discussions resulted in a special issue of the journal Structural Equation Modeling focused on a target article by Hayduk and Glaser followed by several comments and a rejoinder, all made freely available, thanks to the efforts of George Marcoulides.

These discussions fueled disagreement over whether or not structural equation models should be tested for consistency with the data, and model testing became the next focus of discussions. Scholars having path-modeling histories tended to defend careful model testing while those with factor-histories tended to defend fit-indexing rather than fit-testing. These discussions led to a target article in Personality and Individual Differences by Paul Barrett who said: “In fact, I would now recommend banning ALL such indices from ever appearing in any paper as indicative of model “acceptability” or “degree of misfit”.” (page 821). Barrett’s article was also accompanied by commentary from both perspectives.

The controversy over model testing declined as clear reporting of significant model-data inconsistency becomes mandatory. Scientists do not get to ignore, or fail to report, evidence just because they do not like what the evidence reports. The requirement of attending to evidence pointing toward model mis-specification underpins more recent concern for addressing “endogeneity” – a style of model mis-specification that interferes with estimation due to lack of independence of error/residual variables. In general, the controversy over the causal nature of structural equation models, including factor-models, has also been declining. Stan Mulaik, a factor-analysis stalwart, has acknowledged the causal basis of factor models. The comments by Bollen and Pearl regarding myths about causality in the context of SEM reinforced the centrality of causal thinking in the context of SEM.

A briefer controversy focused on competing models. Comparing competing models can be very helpful but there are fundamental issues that cannot be resolved by creating two models and retaining the better fitting model. The statistical sophistication of presentations like Levy and Hancock (2007), for example, makes it easy to overlook that a researcher might begin with one terrible model and one atrocious model, and end by retaining the structurally terrible model because some index reports it as better fitting than the atrocious model. It is unfortunate that even otherwise strong SEM texts like Kline (2016) remain disturbingly weak in their presentation of model testing. Overall, the contributions that can be made by structural equation modeling depend on careful and detailed model assessment, even if a failing model happens to be the best available.

An additional controversy that touched the fringes of the previous controversies awaits ignition. Factor models and theory-embedded factor structures having multiple indicators tend to fail, and dropping weak indicators tends to reduce the model-data inconsistency. Reducing the number of indicators leads to concern for, and controversy over, the minimum number of indicators required to support a latent variable in a structural equation model. Researchers tied to factor tradition can be persuaded to reduce the number of indicators to three per latent variable, but three or even two indicators may still be inconsistent with a proposed underlying factor common cause. Hayduk and Littvay (2012) discussed how to think about, defend, and adjust for measurement error, when using only a single indicator for each modeled latent variable. Single indicators have been used effectively in SE models for a long time, but controversy remains only as far away as a reviewer who has considered measurement from only the factor analytic perspective. Though declining, traces of these controversies are scattered throughout the SEM literature, and you can easily incite disagreement by asking: What should be done with models that are significantly inconsistent with the data? Or by asking: Does model simplicity override respect for evidence of data inconsistency? Or, what weight should be given to indexes which show close or not-so-close data fit for some models? Or, should we be especially lenient toward, and “reward”, parsimonious models that are inconsistent with the data? Or, given that the RMSEA condones disregarding some real ill fit for each model degree of freedom, doesn’t that mean that people testing models with null-hypotheses of non-zero RMSEA are doing deficient model testing? Considerable variation in statistical sophistication is required to cogently address such questions, though responses will likely center on the non-technical matter of whether or not researchers are required to report and respect evidence.

Extensions, modeling alternatives, and statistical kin

 * Categorical dependent variables
 * Categorical intervening variables
 * Copulas
 * Deep Path Modelling
 * Exploratory Structural Equation Modeling
 * Fusion validity models
 * Item response theory models
 * Latent class models
 * Latent growth modeling
 * Link functions
 * Longitudinal models
 * Measurement invariance models
 * Mixture model
 * Multilevel models, hierarchical models (e.g. people nested in groups)
 * Multiple group modelling with or without constraints between groups (genders, cultures, test forms, languages, etc.)
 * Multi-method multi-trait models
 * Random intercepts models
 * Structural Equation Model Trees
 * Structural Equation Multidimensional scaling

Software
Structural equation modeling programs differ widely in their capabilities and user requirements.

title: Structural equation modeling


text:
Say It Like You Mean It

Say It Like You Mean It is the debut studio album by American rock band the Starting Line, following their debut EP With Hopes of Starting Over.... It was released on July 16, 2002.

Background
Guitarist Matt Watts and drummer Mike Golla met while at a mutual friend's band practice. They formed their own band and started searching for a vocalist. The pair looked through AOL's member directory and emailed a number of people. They came across Kenny Vasoli, and subsequently met him while he was playing with his own band. He was drafted into Watts and Golla's band, which broke up after a week. The members remained in contact, and formed the Starting Line in mid-1999 under the name Sunday Drive. Drummer Tom Gryskiewitz was brought into the fold after him and Watts met at a restaurant. Golla subsequently moved to guitar. They wrote material in their practice space and tracked demos. They started gaining publicity with the aid of AOL and MP3.com. Independent label We the People Records became aware of the band's demos and signed them in mid-2000. Watts said they wanted to go with Drive-Thru Records, which was their dream label.

The band recorded an album's worth of material with producer Chris Badami, which was due for release in early 2001. However, it wasn't released due to the intervention of Drive-Thru Records, who saw the band's commercial potential. We the People Records, who had ties with Drive-Thru, had arranged a showcase for the label's founders Stefanie and Richard Reines. The pair were impressed with the band, but thought the songs lacked choruses. The band went away and reworked the material, before signing to Drive-Thru in April 2001. At the time, Vasoli was in high school and Watts was in college. With help from a guidance counsellor, Vasoli graduated early, finishing his last high school year and two semesters at community college. The band changed their name to the Starting Line following threats from a Missouri-based act also called Sunday Drive. The band released the With Hopes of Starting Over... EP in July. Following this, the band became a full-time touring act. As a proposed September 2001 tour with Finch and the Movielife was cancelled following the September 11 attacks, they took October 2001 off to write more songs for their forthcoming debut.

Recording
The Starting Line cancelled their tour dates in January 2002 due to Vasoli contracting mono. Later that month, the band began recording Say It Like You Mean It at Media Vortex with producer Mark Trombino, who Golla said brought "an extra set of ears to the table". Vasoli said the band had wanted to work with Trombino for a while, intentionally waiting for him to be available so they could record with him. They went with him as all of the members' all-time favorite album was Clarity (1999) by Jimmy Eat World, which Trombino produced. Sessions were then delayed due to a family emergency, which resulted in a cancellation of tour dates. Vasoli remarked that he wished he was not sick during recording, "and I would have a voice to sing with. I didn't this time and it was the worst thing ever". "Leaving" and "Saddest Girl Story", two tracks that originally appeared on the With Hopes of Starting Over... EP, were re-recorded for Say It Like You Mean It. "Almost There, Going Nowhere", "Cheek to Cheek", "Left Coast Envy" and "The Drama Summer", which were originally recorded for the We the People album, were also re-recorded.

Nate Barcalow of Finch and Keith Goodwin of Days Away contributed additional vocals; the former on "Cheek to Cheek" and "This Ride", the latter on "Left Coast Envy". "Cheek to Cheek" was originally intended to feature a screaming part, but as Vasoli did not "have a very good scream at all", they enlisted Barcalow, who recorded his part while Finch were recording What It Is to Burn (2002). Vasoli said that since Barcalow was already recording screams for one of the songs, "I just thought it would be cool to have a scream [on "This Ride" ...] I figured why not two?" Goodwin was a friend of Vasoli, while Days Away lived around 10–20 minutes from the Starting Line. Trombino mixed the recordings at The Robot Factory in Los Angeles, California, before they were mastered by Steven Marcussen at Marcussen Mastering in Hollywood.

Composition
Musically, the album drew comparisons to Blink-182, Jimmy Eat World and New Found Glory. The album's title is taken from a line in "Almost There, Going Nowhere". All of the songs were written by the band, except for "The Drama Summer" which was credited solely to Vasoli. The band usually worked on material together through jamming, where they would hear a part they enjoyed and expanded on it. On occasion, Golla or Vasoli arrived at practice with a complete song already written. Vasoli said the "meaner" tracks were about one of his ex-girlfriends. He initially promised not to write a song about her, but ended up writing six tracks. Similarly, "Hello Houston" and "A Goodnight's Sleep" were about a different ex-girlfriend. Vasoli said that despite him not being "that bitter about it anymore", he found it "funny to rehash".

The opening track "Up & Go" details a girl leaving despite having no reason to do so, and was compared to "Anthem Pt. 2" by Blink-182. "Given the Chance" is about the band's fans, specifically the ones in New Jersey. They found it hard to attract an audience in their home state of Pennsylvania, but found it easier in New Jersey. It was reminiscent of the tracks heard on Enema of the State (1999) by Blink-182. "Leaving" sees Vasoli yearning for unrequited love; it references the date February 12, 1999, which Vasoli said was a "really good night" that evolved into the "first really romantic experience I've ever had". "The Best of Me" has an acoustic intro, before shifting into punk rock track. "A Goodnight's Sleep" is a ballad, and was reminiscent of "Eyesore" by New Found Glory. Watts said "Saddest Girl Story" is about a girl he and Vasoli knew from their hometown. "The Drama Summer" is an acoustic emo song in the style of Dashboard Confessional and the Get Up Kids.

Release
On February 6, 2002, Say It Like You Mean It was announced for release in July. In April 2002, the band toured Japan with Planet Smashers and Nicotine. In April and May, the band went on tour with Brand New and Finch; the trek included an appearance at Skate and Surf Fest. Following this, the band went on a UK tour with New Found Glory and Finch. Between late June and mid-August, the band performed on the Warped Tour, appearing on the Drive-Thru stage. Say It Like You Mean It was made available for streaming on July 13, before being released on July 16 as a joint release by Drive-Thru and major label MCA Records. The band went on tour with Reel Big Fish in September and October. On October 27, a music video for "The Best of Me" was posted on Launch.com. The video starts with a guy attempting to impress a girl by playing music from a boombox outside of her residence. When the music stops, the band appear and start performing.

In early and mid-November, the band toured with Taking Back Sunday, the Early November and the Exit, before touring with Park, The Early November and Yellowcard for the remainder of the month. Further touring with Taking Back Sunday, alongside the Reunion Show and Northstar, followed in December. In January 2003, the band went on a tour of Japan with New Found Glory and Good Charlotte, before embarking on a European tour with Reel Big Fish and Sugarcult. To coincide with these shows, Say It Like You Mean It was released in those territories. Between mid-February and late April, they went on a US tour with Sum 41, No Use for a Name and Authority Zero.

A new music video was posted online for "The Best of Me" through MTV.com on June 13. The band went on a UK tour in June with support from From Autumn to Ashes and The Reunion Show. "The Best of Me" was released as a single on June 16. The band performed a few shows with Mae and River City High and Zolof the Rock & Roll Destroyer in early and mid-July. In mid-July and early August, the band appeared on the Warped Tour, playing on the main stage. "The Best of Me" was released to modern rock radio stations on July 22. Between late August and mid-October, the band performed on the Drive-Thru Records 2003 Invasion Tour. On September 8, the band performed on Jimmy Kimmel Live, which was followed by an appearance on IMX. In the same month, a music video was filmed for "Leaving"; it premiered during MTV2's Rock programme in November.

Reception and legacy
AllMusic reviewer Kurt Morris said the record was "full of bubbly, positive lyrics", amidst "plenty of upbeats and catchy hooks." In a review for Rolling Stone, music critic J.D. Considine noted that the band had based their sound on the Green Day "blueprint, with plenty of bright, singalong choruses and hyperstrummed power chords." Despite the comparison to Green Day, he viewed the Starting Line as being more progressive musically and lyrically than them. Ultimate Guitar Archive noted that Vasoli's was deeper compared to the band's earlier works, and called his lyrics heartfelt.

As of July 2007, it has sold close to 300,000 copies. In October 2012, independent label SRC Vinyl released the We the People album under the name The Early Years. Following this, the band went on an anniversary tour for Say It Like You Mean It, during which they performed it in its entirety, in December. In May 2014, the album was re-pressed on vinyl through SRC Vinyl with the bonus tracks "Greg's Last Day" and an acoustic version of "The Best of Me". Later that year, Rock Sound included the album on their The 51 Most Essential Pop Punk Albums of All Time list at number 21. Kerrang! similarly included the album at number 27 on their 51 Greatest Pop-Punk Albums list. In a 2016 listicle, Rob Rousseau of A.Side TV viewed the album as a "masterwork" of the "era-defining Drive Thru Records ouvre." Cleveland.com ranked "The Best of Me" at number 33 on their list of the top 100 pop-punk songs. Alternative Press ranked "The Best of Me" at number 35 on their list of the best 100 singles from the 2000s. Writing in 2022, Andrew Sacher of BrooklynVegan said Vasoli's "yearning, yelpy delivery separated The Starting Line from their snot-nosed pop punk forebears, and when you listen the newer generation of pop punk and emo-pop bands, I'd say you hear even more echoes of Kenny's voice than of Tom DeLonge's or Jordan Pundik's".

Track listing
All songs written by the Starting Line, except "The Drama Summer" by Kenny Vasoli.

Personnel
Personnel per booklet.

The Starting Line
 * Kenny Vasoli – vocals, bass guitar
 * Matt Watts – rhythm guitar
 * Tom Gryskiewicz – drums
 * Mike Golla – lead guitar

Additional musicians
 * Nate Barcalow – additional vocals (tracks 7 and 13)
 * Keith Goodwin – additional vocals (track 11)

Production
 * Mark Trombino – producer, engineer, mixing
 * Steven Marcussen – mastering
 * Tim Stedman – art direction, design
 * Marco Orozco – design
 * Micah Panzich – design
 * Justin Stephens – photography

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Say It Like You Mean It


text:
Talk:Green Line (Washington Metro)

Let's turn this list around
In the interest of promoting uniformity, I find it would be beneficial to turn the list of Green Line stations around so as to list them from south to north. This would harmonize with the existing sections for the Blue Line, Orange Line, and Red Line, which all list their stations south-to-north and west-to-east.

The Yellow Line is also listed north-to-south, and I am also separately proposing changing that line's station list around to list south-to-north.

green line shortcut
I'd like to see an article or sub-article on the Green Line Shortcut. I had always heard of it, but living in NoVA and staying mainly on the Orange Line, I never rode it. I'd like to know more about it... --Phil Kirlin 22:09, 20 November 2005 (UTC)

 * I dunno what more info we can have on it that isn't already here.. what more do you want to know? --Golbez 22:43, 20 November 2005 (UTC)

 * I tend to agree - there's not that much else to say about it. Trains used the B&E connection to go from the E Route (Green Line) to the B Route (Red Line) and back, and terminated at the pocket track at Farragut North. SchuminWeb (Talk) 18:50, 21 November 2005 (UTC)

 * Here are some possible questions.
 * Where is the spur that was once used for the shortcut? Can you see it when you're riding the Green or Red Lines? Can you see it in an aerial photograph?
 * When it was in operation, did all Green Line trains take it? Did the Green Line ever even stop at Fort Totten? Did the shortcut run in both directions? Did it run all day, or only during rush hour?
 * Why stop it? Even though the Green Line middle section was eventually finished, it seemed pretty popular. After all, everyone who works in DC works near Farragut North, right? :)
 * What is a pocket track?
 * --PKirlin 22:28, 21 November 2005 (UTC)

 * To answer your questions:

 * The B&E connection is right around the Fort Totten station. The opening for the Red Line end of it is above ground just south of Fort Totten. There's an interlocking connecting both tracks to a third track that descends underground. That's the B&E track, and they also use it like a pocket track to turn trains around when they terminate trains at Brookland-CUA. On the Green Line side, it's only on Track 1 (Greenbelt side), and it is in the tunnel just north of Fort Totten. As for seeing it from the train, I've not seen it, but I've also not been looking for it.

 * Whether all Green Line trains took it or not, I don't know. I didn't ride the Green Line too much back then.

 * Why stop it? It was never intended as a permanent solution, and the connection was not designed for revenue service. Its purpose, along with the A&C connection near the two "Farragut" stations, is to allow trains to be moved to and from the Red Line and the rest of the system. This was also the only connection to the system that the outer Green Line had with the rest of the system before the mid-city segment opened. The purpose of running the commuter shortcut was to get outer Green Line riders to downtown Washington without having to make a transfer at Fort Totten. This is now possible on the Green Line without the shortcut, as riders can go downtown via Gallery Place-Chinatown and Archives-Navy Memorial.

 * Lastly, a pocket track is a third track connected to both sides that's used for train storage and to turn back trains. File:WMATA D Route Pocket Track.jpg shows the D Route pocket track. Pocket tracks are regularly used at Grosvenor, Silver Spring, and Mt. Vernon Square. At these stations, the train is offloaded (put out of service), it moves into the pocket track, and then resumes service in the other direction.

 * Hope that helps! SchuminWeb (Talk) 09:07, 22 November 2005 (UTC)

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 15:34, 9 November 2007 (UTC)

usage of "the" before WMATA (correction questioned)
This little bit bothered me enough to try and find something online that can back the word "the" being used before the acronym WMATA.

I came across this link quickly that noted as follows:

 * Don't use the before acronyms pronounced as words instead of letter by letter: OSHA, CAD. With other abbreviations, apply the same rules for the full name and the shortened version: the ESA, the state DOT, IBM. When placing either a or an before an abbreviation or acronym, determine how it would sound when spoken; see a, an, the entry above.

Thus being, isn't "the WMATA" correct?

I welcome anothers spin on this. I was converted regarding the "composed/comprised" argument way back...with proper references why not to.

--Allamericanbear (talk) 17:37, 11 June 2011 (UTC)

 * I think it might be if "WMATA" were pronounced W-M-A-T-A, i.e. as individual letters. Most common usage is pronouncing the acronym as a single three-syllable word, rhyming with "cantata". Thus you would say "Richard Sarles is the head of WMATA" and not "Richard Sarles is the head of the WMATA". If it were pronounced as initials, then the latter usage would be correct. But it's because it gets pronounced as a word. Make sense? SchuminWeb (Talk) 18:13, 11 June 2011 (UTC)

 * Not understanding, likely because I'm not a local to DC. Locally, in Buffalo NY, I refer to the NFTA as the N-F-T-A, not "nifta" or whatever clever wording people come up with. But, really? People call it wah-mah-ta? I'd say to hell with it and call it Washington Metro.

--Allamericanbear (talk) 19:25, 11 June 2011 (UTC)

 * I lived in DC for ten years and never heard "W-mah-tah"; on the other hand, I never heard "the WMATA" either, since it's not exactly an entity that gets brought up often in discussion. :P I've always said "the WMATA". And allamericanbear, that's incorrect; "WMATA" is not the Washington Metro. It's the umbrella organization. That would be like saying "to hell with calling it FBI, call it the Department of Justice." --Golbez (talk) 23:02, 11 June 2011 (UTC)

 * I checked into that. According to the article Washington Metropolitan Area Transportation Authority, it's listed as saying:

 * The Washington Metropolitan Area Transit Authority (often abbreviated as WMATA and commonly referred to as Metro). I'd believe that, however, a lot faster than it being called "wuh-ma-ta". Can someone actually source that, please??

 * As for my earlier question, can someone SOURCE the reason for the change in grammar so that this can be put to rest? I, when changing most grammatical errors, VERIFY so that it can be handled in as few comments as possible? My earlier comment stated "with proper references why not to". I'm not accusing anyone of being an English major (not that it's a bad thing), but it would be appropriate to have it backed from a reliable source, instead of someone's gut feeling that it's wrong. What I read on the source I provided, I'm understanding it differently than you may.

 * --Allamericanbear (talk) 23:30, 11 June 2011 (UTC)

 * I've lived in D.C. since 1988, and it's always been pronounced "wuh-MAT-uh" as far as I can tell. Local television news does so, as does the local press. For example, in a report on today's bomb threat at the Rockville station, NBC-4 did not use the article "the" before WMATA. In a WUSA-9 report on subway cars without air conditioning on June 8, that TV station did not use the "the" either. Nor did The Washingtonian in a June 3 article about manual operation of subway cars, nor did the Washington Post in a May 26 article on a Metro police assault on a handicapped man or a May 20 article on rising WMATA parking fees. Zachary M. Schrag, in his The Great Society Subway: A History of the Washington Metro, uses it without the "the" unless it is used adjectivally. The article "the" would only be used with WMATA when referring to a noun in which WMATA would be an adjective. For example: "the WMATA board" or "the open WMATA General Manager position," "the WMATA system map," or "the WMATA press release." As for a source for this, I do not have access to WMATA's style guide. The Chicago Manual of Style (which Wikipedia's own Manual of Style cites) at 15.9 says "Acronyms are read as words and, except when used adjectivally, are rarely proeceded by a, an, or the ('member of nations NATO'). Initialisms are read as a series of letters and are often preceded by an article ('member nations of the EU')." I've never heard of WMATA referred to as anything but an acronym. - Tim1965 (talk) 15:23, 13 June 2011 (UTC)

Personally, I would say, absent a video or source of a WMATA official saying "W-ma-tah", we should go with the avenue of least confusion, which in this case appears to be "the WMATA". They might do it that way, but we can only report on verifiable things, and it does appear that omitting "the" without a sourced reason is confusing to readers. --Golbez (talk) 15:25, 13 June 2011 (UTC)
 * ^^^ awesome timing. :P Given that sourcing, I suppose I'm forced to agree with omitting 'the' where it can be read out. --Golbez (talk) 15:32, 13 June 2011 (UTC)

 * You can hear members of Congress (including D.C. Delegate Eleanor Holmes Norton) and WMATA chairman Jim Graham and WMATA General Manager John Catoe calling it "wuh-MAH-tuh" in this Congressional hearing. (As all YouTube sites are now blocked by Wikipedia, do a search on YouTube for "Washington Metropolitan Area Transit Authority (WMATA) Hearing Panel 1" or "4-29-09 OGR Federal Workforce Subcommittee".) - Tim1965 (talk) 15:46, 13 June 2011 (UTC)

 * I've seen the video, and it actually surprised me that they call WMATA as if the acronym is a word, but isn't the point of this also that a local or regional depiction of what it's called does not make it appropriate? I'm looking at the general public as a whole. Hearing "Wuh-ma-ta" in someone's conversation does not immediately send me to think that it's meant to be the WMATA. I'm looking at the population that reads it from other places (since this is a world accessible wiki). In that case, I suggest as I provided (with citation):

 * With other abbreviations, apply the same rules for the full name and the shortened version, the ESA, the state DOT, IBM.

 * I'm looking at it as the same as not calling the ESA "esa" or IBM "ibbum". Local jargon should be avoided, and if it's mentioned, it should be noted that "also referred to as "Wuh-mah-ta by locals".
 * Chicago Manual of Style, which is far more authoritative, makes a clear distinction between initialism and acronyms. WMATA is not an initialism. This is not a matter of local usage. National political leaders call it WMATA. Just as it's "NAY-toh" and not "En-ay-tee-oh" nor "the NATO." Your rationale, it seems, would have us ignore the distinction between acronyms and initialisms, which are highly dependent on usage. Usage nationally and locally favors "WUH-mah-ta" and without the article "the". - Tim1965 (talk) 19:00, 13 June 2011 (UTC)

 * You're saying "locally" and "nationally" favoring. Is this proper English though?

 * --Allamericanbear (talk) 20:58, 13 June 2011 (UTC)

 * Thank you for the comparison to NATO. Excellent point. SchuminWeb (Talk) 03:00, 14 June 2011 (UTC)

 * The way I've described is also the way The Great Society Subway refers to WMATA. SchuminWeb (Talk) 19:22, 13 June 2011 (UTC)

 * If ya's insist on it, let it be then. I just think that comparing NATO and WMATA is like apples and oranges. It's clearly not in the general public's common language.

 * Just, PLEASE don't "niftay" the NFTA!!! It's far from that. Cheers.

 * --Allamericanbear (talk) 03:47, 14 June 2011 (UTC)

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 * Added archive https://web.archive.org/web/20110615184927/http://www.wmata.com/about_metro/news/PressReleaseDetail.cfm?ReleaseID=2546 to http://www.wmata.com/about_metro/news/PressReleaseDetail.cfm?ReleaseID=2546
 * Added archive https://web.archive.org/web/20100113080825/http://wmata.com/about_metro/docs/media_guide_2009.pdf to http://www.wmata.com/about_metro/docs/media_guide_2009.pdf
 * Added archive https://web.archive.org/web/20101227224335/http://wmata.com/community_outreach/lunchtalk_online_chats/transcript.cfm?ChatID=184 to http://www.wmata.com/community_outreach/lunchtalk_online_chats/transcript.cfm?ChatID=184
 * Added archive https://web.archive.org/web/20110718074753/http://wmata.com/pdfs/rail/weekday_evenings.pdf to http://www.wmata.com/pdfs/rail/weekday_evenings.pdf
 * Added archive https://web.archive.org/web/20100131065428/http://wmata.com/rail/parking/parking_detail.cfm?station=85 to http://www.wmata.com/rail/parking/parking_detail.cfm?station=85
 * Added archive https://web.archive.org/web/20101110160451/http://mta.maryland.gov/services/bus/schedule/LRMAP209.pdf to http://mta.maryland.gov/services/bus/schedule/LRMAP209.pdf

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Dedicated Crime Section
I'm curious if others think having a dedicated crime section on this page is warranted, given that none of the other WMATA line pages have a similar section. There have been acts of violence throughout the system, so it would seem better to have this information on the Metro page itself, rather than called out here. Shouldn't there be some consistency among the pages for the different lines? As noted by the "needs updating" tag, the data also is stale, and the section frequently mentions stations served by lines other than the Green, and in some cases, are not Green line stations at all.--RCSpengler (talk) 03:30, 16 July 2020 (UTC)

Requested move 22 January 2024

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Procedural close. Interested editors should comment in the consolidated discussion at Talk:Red Line (Washington Metro). (closed by non-admin page mover) Adumbrativus (talk) 02:54, 22 January 2024 (UTC)

Green Line (Washington Metro) → Green line (Washington Metro) – Lowercase the word “line” per WP:NCCAPS. The word “line is a generic descriptor. 2600:1700:1960:F100:A882:B52C:C11A:62E9 (talk) 02:14, 22 January 2024 (UTC) The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Move discussion in progress
There is a move discussion in progress on Talk:Red Line (Washington Metro) which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 03:02, 22 January 2024 (UTC)

title: Talk:Green Line (Washington Metro)


text:
Ford Motor Credit Company

Ford Motor Credit Company LLC, d/b/a Ford Credit, is the financial services arm of Ford Motor Company, and is headquartered in Dearborn, Michigan.

The predominant share of Ford Credit's business consists of financing Ford and Lincoln vehicles and supporting Ford and Lincoln dealers. Specifically, its business activities are concentrated in the area of automobile financing for consumers and dealership inventory and leasing. Ford Credit competes mainly on the basis of service and financing rate programs, including those sponsored by Ford. A key foundation of its service is providing broad and consistent purchasing policies for retail installment sale and lease contracts, and consistent support for dealer financing requirements across economic cycles. These policies have helped Ford Credit build strong relationships with Ford's dealer network that enhance competitiveness. Ford Credit also provides commercial financing and lines of credit to dealerships selling Ford Motor Company products. The firm also issues commercial paper and other debt instruments on Ford's behalf.

Ford Credit also owns Lincoln Automotive Financial Services, the arm that finances Lincoln vehicles.

Ford earned $2.63 billion EBIT with its Ford Credit segment in 2018, up from $2.31 billion in 2017. 2018 was the segment's highest full-year EBT in eight years. However, this upward trend may not last much longer as car sales continue to decline. Ford Credit's ROE, which fell from 22% in 2017 to 14% in 2018 forecasts the segment's coming decline.

History
Ford began its journey into auto financing by launching a Weekly Purchase Plan in 1923. The program was designed to allow people to pay a certain amount to the bank weekly up until they had saved for the cost of a car. In 1926, Ford constructed a new factory in Germany, but most of the local population could not afford a car. This prompted Henry Ford to found Credit AG für Ford-Fahrzeuge, German for ' Ford Credit Company AG', in Berlin in order to help locals finance the purchase of a new car, in turn increasing sales. Henry and Edsel Ford became members of the board. In 1932, the newly-founded bank and the factory moved to Cologne. In 1962 the bank was renamed again to Ford Credit AG.

From 1975 to 1979, the company briefly was the owner of the Houston Astros major league baseball team, as well as of its ballpark, the Astrodome, and various other properties around Houston, Texas. This occurred after Astros owner Roy Hofheinz defaulted on a loan provided in 1972 by the Company in partnership with GE Capital. The default resulted from a downturn in the oil industry, and the creditors took over these various assets as a result. Senior loan officer Bill Odom, who would later rise to be the Chairman of Ford Motor Credit Company, acted as principal for the temporary ownership group, until the team was sold in 1979 to a group headed by John McMullen.

Since the automotive industry crisis of 2008–10, Ford Credit has been the only financial arm of Detroit's "Big Three" still owned by its parent automaker after the spinoff of GMAC (now Ally Financial) by General Motors and the purchase of Chrysler Financial (now TD Auto Finance) by Toronto-Dominion Bank.

title: Ford Motor Credit Company


text:
Sydney Ducks

The Sydney Ducks was the name given to a gang of criminal immigrants from Australia in San Francisco, during the mid-19th century. Because many of these criminals came from the well-known British penal colonies in Australia, and were known to commit arson, they were blamed for an 1849 fire that devastated the heart of San Francisco, as well as the rampant crime in the city at the time.

The Sydney Ducks were criminals who operated as a gang, in a community that also included sailors, longshoremen, teamsters, wheelwrights, shipwrights, bartenders, saloon keepers, washerwomen, domestic servants, and dressmakers. The largest proportion (44%) were born in Ireland and migrated during the Great Irish Famine, first to Australia as laborers and then to California as part of the Gold Rush.

The criminality of the Sydney Ducks was the catalyst for the formation of the first Committee of Vigilance of 1851. The vigilantes usurped political power from the corrupt or incompetent officials in the city, conducted secret trials, lynchings, and deportations, which effectively decimated the Sydney Ducks. The area where the Sydney Ducks clustered at the base of Telegraph Hill was originally known as "Sydney-Town," but by the 1860s was called exclusively by its better-known name, the Barbary Coast.

On December 19, 1854, five members of the gang were involved in the Jonathan R. Davis fight.

title: Sydney Ducks


text:
Talk:Yellow Line (Washington Metro)

Let's turn this list around
In the interest of promoting uniformity, I find it would be beneficial to turn the list of Yellow Line stations around so as to list them from south to north. This would harmonize with the existing sections for the Blue Line, Orange Line, and Red Line, which all list their stations south-to-north and west-to-east.

The Green Line is also listed north-to-south, and I am also separately proposing changing that line's station list around to list south-to-north.

 * I disagree with your premise; the Blue and Orange lines are predominantly West/East, and the Red Line has two northern termini, so I used W->E there too. The main reason for these were for the boxes at the bottom of each station; I wanted the west station to be the previous station, and therefore be on the LEFT (west) side of the box. The Green Line has two eastern termini, so either N->S or S->N must be used, and Yellow is predominantly north/south though it does have NE and SW termini (terminuses?). That the other lines do theirs S->N is a byproduct of the fact that they are PRIMARILY West->East.

 * And looking at it from a purely aesthetic point of view - we have a map right there with north on the top and south on the bottom. It would look backwards to have, in the list, south on the top and north on the bottom.

 * Finally, please sign your comments by typing ~ . --Golbez 07:43, Jun 8, 2005 (UTC)

 * First of all, my apologies for not signing. It completely slipped my mind to sign the post, and was not intentional.

 * In changing the Yellow Line's direction, as we are on that page, this makes it harmonize with the Blue Line. The section of the C Route where the Blue and Yellow Lines each run trains is a predominantly north-south alignment. In the articles on the individual stations, the station to the south is listed as "preceding" and the station to the north is listed as "following". Then, if one follows the articles one after the other, when one reaches L'Enfant Plaza, the first station going north that is shared with the Green Line, the presumed "travel direction" changes, and the next station north becomes "preceding". I find that if we are describing a system where all lines except the Red Line share at least a small section of track with another line, keeping things uniform is quite important.

 * Additionally, I don't believe that starting the list for the Green and Yellow Lines at the south is too far-fetched. The mileposts on the Interstate highway system begin numbering from the southern end of the highway and work their way north. Additionally, at the top of the official WMATA system map, the Yellow Line is listed as running from Huntington to Mt. Vernon Square, and the Green Line is listed as running from Branch Avenue to Greenbelt.

 * Schuminweb 05:41, 10 Jun 2005 (UTC)

 * The core line is Orange. That is the most obviously West to East line. Blue piggybacks on it; therefore, Blue must be west to east, which makes the western half South to North. Since Yellow piggybacks on it, that means Yellow must be south to North, and since Green joins Yellow, Green must be South to North.

 * Fair enough. Incidentally, I once saw something like this, but where can I find out what Routes there are? (You mention the C Route) --Golbez 17:05, Jun 10, 2005 (UTC)

 * Awesome. I'll implement the changes.

 * As for the routes, they are as follows:
 * A Route: Shady Grove Yard (just beyond Shady Grove station) to center of platform at Metro Center upper level
 * B Route: Center of platform at Metro Center upper level to Glenmont Yard (just beyond Glenmont station)
 * C Route: Huntington to the center of the lower level platform at Metro Center via King Street and Arlington Cemetery
 * D Route: Center of Metro Center lower level platform to New Carrollton
 * E Route: Center of lower level platform at Gallery Place-Chinatown to Greenbelt Yard (just beyond Greenbelt station)
 * F Route: Branch Avenue Yard (just beyond Branch Avenue station) to the center of the lower level platform at Gallery Place-Chinatown
 * G Route: D&G junction east of Stadium-Armory (just beyond the pocket track, where the Blue Line separates and goes underground) to just beyond Largo Town Center station
 * H Route: Non-existent
 * I Route: Non-existent
 * J Route: Just beyond Franconia-Springfield station to just south of King Street at the C&J junction (where the Blue and Yellow Lines join)
 * K Route: Just west of Vienna/Fairfax-GMU station to the C&K junction just south of Rosslyn (where the Blue and Orange lines join)
 * L Route: Just north of Pentagon station at the C&L junction (where the Blue and Yellow Lines diverge) to just south of L'Enfant Plaza station at the E&L junction (where the Green and Yellow lines join)

 * Schuminweb 03:08, 12 Jun 2005 (UTC)

Fort Totten
So do we add the Yellow Line extension now, or do we wait til January? It's different than with Silver line, since that's an entire new line, and therefore easily divorced from the real system. But this would have to have disclaimers with each station until Jan 07 saying "not yet!" --Golbez 21:40, 25 April 2006 (UTC)
 * Would add the mention and the soure links, but i would not make changes to the station lists or maps and such untill it happens, with it being announced to early, it can be tabled before it ever happens. --Boothy443 | trácht ar 03:00, 26 April 2006 (UTC)
 * Indeed, I'd be inclined to wait for now as well. SchuminWeb (Talk) 21:55, 26 April 2006 (UTC)

'On to Greenbelt'. Should we note that there are two Yellow Line trains on weekdays that run all the way to Greenbelt? They leave Huntington Station at 2:37pm and 2:49pm (I actually used the Metro RideGuide site to find the scheduled times of the two trains. SterlingNorth 01:05, 18 March 2007 (UTC)
 * We have a proper citation for it, why not? SchuminWeb (Talk) 09:12, 18 March 2007 (UTC)

External links modified
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External links modified (January 2018)
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 * Added archive https://www.webcitation.org/6HNIh4uSL?url=http://www.wmata.com/about_metro/docs/history.pdf to http://www.wmata.com/about_metro/docs/history.pdf
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Requested move 22 January 2024

 * The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.

The result of the move request was: Procedural close. Interested editors should comment in the consolidated discussion at Talk:Red Line (Washington Metro). (closed by non-admin page mover) Adumbrativus (talk) 02:54, 22 January 2024 (UTC)

Yellow Line (Washington Metro) → Yellow line (Washington Metro) – Lowercase the word “line” per WP:NCCAPS. The word “line is a generic descriptor. 2600:1700:1960:F100:A882:B52C:C11A:62E9 (talk) 02:15, 22 January 2024 (UTC) The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Move discussion in progress
There is a move discussion in progress on Talk:Red Line (Washington Metro) which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 03:02, 22 January 2024 (UTC)

title: Talk:Yellow Line (Washington Metro)


text:
Talk:Samantha Geimer

I've done a partial merge. Anyone think more should be moved? --ssd 04:15, 8 Jun 2005 (UTC)

No, I think this deserves its own article. And I have to question the wording, she was not the victim of statutory rape, but of rape. Polanski was convicted of statutory but that does not reflect the facts of the case. protohiro 17:17, 22 July 2005 (UTC)

I'd agree that it should be expanded into its own article. Mbisanz 17:24, 22 July 2005 (UTC)

I disagree - this should be mergeed, since Samantha Geier is only notable for having been raped by Polanski.XmarkX 16:01, 24 July 2005 (UTC)

As it stands, this article might as well be deleted. TheMadBaron 10:41, 9 August 2005 (UTC)

I would agree with a merge/delete Sherurcij 18:03, August 9, 2005 (UTC)

I would agree with a merge/delete/redirect; I agree with XmarkX. Tempshill 22:44, 9 August 2005 (UTC)

Her only notariety comes from (according to the Roman Polanski article) having been drugged and raped by a celebrity. I think delete and allow her to be mentioned only in the one article where she's relevant. 12:05, 10 August 2005 (UTC) or 7:05 pm (CST)

I would Suggest keeping the Article, as it shows that Victim of Rape is not the only Victimization, ... as The Judge and Defense made attacks and False Claims .. as did the Media Telling more Lies than the Son of Satan. She was Victimized 3 times ... and this should be made visible to and by any with Intergrity.

Julle geimer
Pellaa youtubessa hill climb racing2 ja critical opssia 109.240.11.214 (talk) 21:18, 9 April 2022 (UTC)

title: Talk:Samantha Geimer