Paul-Gauthier Noé

Titouan Parcollet

Mohamed Morchid

CGCNN: COMPLEX GABOR CONVOLUTIONAL NEURAL NETWORK ON RAW SPEECH

Keywords: SincNet, complex neural networks, Gabor filters, speech recognition

Convolutional Neural Networks (CNN) have been used in Automatic Speech Recognition (ASR) to learn representations directly from the raw signal instead of hand-crafted acoustic features, providing a richer and lossless input signal. Recent researches propose to inject prior acoustic knowledge to the first convolutional layer by integrating the shape of the impulse responses in order to increase both the interpretability of the learnt acoustic model, and its performances. We propose to combine the complex Gabor filter with complexvalued deep neural networks to replace usual CNN weights kernels, to fully take advantage of its optimal time-frequency resolution and of the complex domain. The conducted experiments on the TIMIT phoneme recognition task shows that the proposed approach reaches top-of-the-line performances while remaining interpretable.

INTRODUCTION

The task of Automatic Speech Recognition (ASR) is far from being solved and represents an active research field [START_REF] Battenberg | Deep speech 2: End-to-end speech recognition in english and mandarin[END_REF][START_REF] Ravanelli | The pytorch-kaldi speech recognition toolkit[END_REF][START_REF] Watanabe | Espnet: End-to-end speech processing toolkit[END_REF][START_REF] Li | Jasper: An end-to-end convolutional neural acoustic model[END_REF]. More precisely ASR systems are either hybrid DNN-HMM, with multiple sub-blocks trained separately [START_REF] Povey | The kaldi speech recognition toolkit[END_REF][START_REF] Ravanelli | Improving speech recognition by revising gated recurrent units[END_REF], or End-to-End (E2E), with various Neural Networks (NN) learnt accordingly to a joint training procedure [START_REF] Graves | Towards end-to-end speech recognition with recurrent neural networks[END_REF][START_REF] Zhang | Towards end-to-end speech recognition with deep convolutional neural networks[END_REF][START_REF] Kim | Joint ctc-attention based end-to-end speech recognition using multi-task learning[END_REF]. Despite numerous architectures and training investigations, the input feature representation remains mostly unchanged with traditional handcrafted acoustic features such as Mel-filter-banks.

Nonetheless, another field of speech recognition recently obtained promising performances while operating at the raw waveform level [START_REF] Palaz | End-to-end phoneme sequence recognition using convolutional neural networks[END_REF][START_REF] Tüske | Acoustic modeling with deep neural networks using raw time signal for lvcsr[END_REF][START_REF] Hoshen | Speech acoustic modeling from raw multichannel waveforms[END_REF][START_REF] Zeghidour | End-to-end speech recognition from the raw waveform[END_REF]. In these works, Convolutional Neural Networks (CNN) have been used directly on the raw speech signal to rapidly consume the large number of data points (e.g. 16, 000 per second for an audio sampled at 16kHz). Unfortunately, and as demonstrated in [START_REF] Ravanelli | Speaker recognition from raw waveform with sincnet[END_REF][START_REF] Ravanelli | Speech and speaker recognition from raw waveform with sincnet[END_REF] traditional CNN kernel filters are not efficient at learning common acoustic features due to the lack of constraint on neural parameters. To alleviate the latter issue, the authors proposed a novel convolutional layer named SincNet incorporating prior speech processing knowledge in an efficient and interpretable operation. More precisely, SincNet filters are initialized and constrained following specific acoustic filters to produce easily interpretable filtering of the input waveform [START_REF] Ravanelli | Speaker recognition from raw waveform with sincnet[END_REF]. As a matter of fact, processing the raw waveform theoretically has numerous advantages including a higher richness of the input signal alongside with a lossless natural representation of the features. Recently, other filters have been proposed for Sinc-Net to further increase its performances [START_REF] Loweimi | On learning interpretable cnns with parametric modulated kernel-based filters[END_REF]. In the latter, Gaussian filters have been suggested without motivations on their major properties in terms of time and frequency localization [START_REF] Gabor | Theory of communication[END_REF]. Furthermore, the authors only proposed to consider the real-part to feed the standard SincNet architecture. We propose to extend this work to the complete complex Gabor filters to take advantage of both the complex-valued representation and a better time-frequency resolution due to the Gaussian shape. Other recent works have used Gabor filters instead of the triangular ones to operate over FBANK acoustic features [START_REF] Robertson | Improving speech recognition with drop-in replacements for f-bank features[END_REF]. In this case, cutoff frequencies of the filters are fixed on the Mel-scale and require fine tuning. Gabor filters have also been used to initialize end-to-end filterbanks learning [START_REF] Schatz | Learning filterbanks from raw speech for phoneme recognition[END_REF]. In the latter works, the filter frequency positions are fixed. We propose to learn all these parameters jointly to the rest of the neural network model to allow the Gabor filters to perfectly match the considered task.

Nonetheless, complex Gabor filters produce a complexvalued filtered signal that must be processed with a dedicated complex-valued model to further fully exploit this input representation. Fortunately, Complex-Valued Convolutional Neural Networks (CVCNN) have been recently introduced with applications to image and speech processing [START_REF] Trabelsi | Deep complex networks[END_REF][START_REF] Huh | Phase-aware speech enhancement with deep complex u-net[END_REF]. Thus, we propose to enhance the original real-valued SincNet with the proposed complex Gabor filters, and to process the filtered signal with a CVCNN respectful of the complex algebra. Contributions of the paper are summarized as:

1. The optimal time and frequency localization compromise of Gabor filters is presented (Section 2).

2. SincNet [START_REF] Ravanelli | Speaker recognition from raw waveform with sincnet[END_REF] is extended to the complex-valued space with a complex Gabor filter and CVCNNs. The model is also released for reproducibility1 (Section 3). 3. Evaluate and analyse the proposed complex gaborbased SincNet on a phoneme recognition task with the TIMIT dataset (Section 4).

The conducted experiments show that our approach reaches promising performances with a natural and efficient filtered representation of the raw waveform, while retaining the interpretability property of the original SincNet.

UNCERTAINTY PRINCIPLE AND GABOR FILTERING

This section motivates the use of Gabor filters to replace the standard sinc approach of SincNet [START_REF] Ravanelli | Speaker recognition from raw waveform with sincnet[END_REF]. First, it is important to notice that time-frequency resolution is limited by the uncertainty principle. More precisely, the product of the time and frequency spread of a filter is superior to a constant. Given any function y ∈ L 2 (R) and its Fourier transform ŷ, their time e y and frequency e ŷ localizations are respectively:

e y = 1 ||y|| 2 +∞ -∞ t|y(t)| 2 dt. e ŷ = 1 ||ŷ|| 2 +∞ -∞ f |ŷ(f )| 2 df. (1)
Then, their time and frequency spreads are defined by their variance v y and v ŷ :

v y = 1 ||y|| 2 +∞ -∞ (t -e y ) 2 |y(t)| 2 dt. v ŷ = 1 ||ŷ|| 2 +∞ -∞ (f -e ŷ ) 2 |ŷ(f )| 2 df. (2)
The uncertainty principle states that v y v ŷ ≥ 1 16π 2 [START_REF] Mallat | A Wavelet Tour of Signal Processing: The Sparse Way[END_REF]. Thus a function can not have an infinite narrow localization both in time and frequency domain. However, this inequality becomes an equality for Gaussian shape functions such as Fig. 2: Illustration of the frequency response of the complex Gabor filter with f 1 and f 2 respectively the low and high cutoff frequencies.

Gabor filter [START_REF] Mallat | A Wavelet Tour of Signal Processing: The Sparse Way[END_REF] and thus provides the best time-frequency resolution compromise.

In particular, the complex impulse response of the Gabor filter is defined as follows:

g(t) = w σ (t)e i2πf0t , = g e (t) + ig o (t), w σ (t) = 1 √ 2πσ e -t 2 2σ 2 , (3)
with σ the standard deviation of the temporal Gaussian window w σ (t), f 0 the center frequency of the filter and g e (t) and g o (t) the real and imaginary part of the impulse response respectively (Figure 1). The Gabor filter has the following Gaussian frequency response:

G(f ) = e -2π 2 σ 2 (f -f0) 2 . ( 4
)
For the sake of interpretability, it is feasible to express σ and f 0 in terms of the cutoff frequencies: Traditional parametric CNNs operate over the raw waveform by performing multiple time-domain convolutions between the input signal and a certain finite impulse response. Therefore, SincNet [START_REF] Ravanelli | Speaker recognition from raw waveform with sincnet[END_REF] proposes to use a sinc function to obtain the impulse response h(t) at time t of a CNN as:

σ = A π(f 2 -f 1 ) , f 0 = f 1 + f 2 2 , (5)
h(t) = 2f 2 sinc(2πf 2 t) -2f 1 sinc(2πf 1 t), (6)
with sinc(x)=sin(x)/x, f 1 and f 2 the two cutoff frequencies and f 2 ≥ f 1 . Such filter has a rectangular frequency response described as:

H(f ) = rect 2f2 (f ) -rect 2f1 (f ), (7)
with rect w (.) the rectangular function of width w centered in 0. Finally, cutoff frequencies are the two only trainable parameters reducing drastically the number of neural parameters compared to CNNs. Then, multiple CNN layers are stacked to reduce the signal dimension, before being fed into a classifier.

Complex Gabor Filtering with CVCNN

We propose to replace the sinc based filter of Eq. 6 with a complex-valued Gabor one, for a better time-frequency resolution. Therefore, let g(t) be the complex Gabor filter impulse response with g e (t) and g o (t) the corresponding real and imaginary parts. The convolution of an input signal x(t) with g(t) at time t is written as:

x(t) * g(t) = x(t) * g e (t) + i(x(t) * g o (t)). (8)
The obtained filtered signal is of the form z = a + ib lying on the complex plane, and is an approximation of analytic signal (i.e. without negative frequencies) [START_REF] Sommer | Geometric Computing with Clifford Algebras[END_REF]. We propose to fully take this complex representation into consideration by further processing it with complex-valued neural networks layers only.

Therefore, the extracted features are then fed into multiple CVCNNs followed by complex layer-normalization to reduce the signal dimension. Finally, the reduced complex features are fed into a complex fully-connected classifier (CVDNN). In the same manner as SincNet [START_REF] Ravanelli | The pytorch-kaldi speech recognition toolkit[END_REF], the two cutoff frequencies of the filters are the only parameters learnt in the first layer, thus reducing the number of neural parameters.

EXPERIMENTS

The proposed approach is evaluated on the TIMIT phoneme recognition task [START_REF] Garofolo | Darpa timit acoustic-phonetic continous speech corpus cdrom[END_REF]. The latter dataset is composed of a standard 462-speaker training dataset, a 50-speakers development dataset and a core test dataset of 192 sentences. During the experiments, the dialect sentences of the training dataset are removed.

Models Achitecture

Our model starts with four CVCNNs with respectively 128, 60, 60 and 60 complex filters of kernel size 129, 5, 5, 3 with Complex Gabor filters used at the first layer only. Then, a Complex-Valued Multilayer Perceptron (CMLP) composed of 5 layers with 1024 complex hidden units is added. The ReLU activation function [START_REF] Nair | Rectified linear units improve restricted boltzmann machines[END_REF] is used accross all the layers. Complex layer-normalization is done on each layer of the CVCNN, while complex batch-normalization is applied on the CMLP layers. Maxpooling is applied on the convolutional part to further reduce the dimension of the signal. Finally the sof tmax function is applied to obtain the posterior probability over the HMM states. Monophone regularization is also used to smooth the training [START_REF] Bell | Regularization of contextdependent deep neural networks with contextindependent multi-task training[END_REF].

We propose to compare this approach with a real-valued equivalent baseline. Thus, the input layer has the same number of filters. Then, the dimensions of the other layers are increased to obtain a comparable number of neural parameters 20M .

Both models are fed with 200ms speech signal chunks with an overlap of 10ms. They are trained using standard stochastic gradient descent with a batch size of 128 for 20 epochs. The learning rate is annealed with respect to a certain threshold on the validation loss evolution, alleviating the risk of overfitting and ensuring an optimal convergence for both models. A dropout probability of 0.15 is also set for each layer except the classification ones.

Models and experiments are run within the Pytorch-Kaldi toolkit [START_REF] Ravanelli | The pytorch-kaldi speech recognition toolkit[END_REF].

Results and Discussions

Models are evaluated by averaging the Phone Error Rate (PER) observed on the validation and test datasets for 5 runs with the TIMIT phoneme recognition task [START_REF] Garofolo | Darpa timit acoustic-phonetic continous speech corpus cdrom[END_REF]. Results are shown in Table 1.

First, it is worth underlying that the obtained results are comparable to state-of-the-art performances on the TIMIT task from the raw waveform. Then, while both real and complex-valued Gabor models obtain similar averaged performances, a best PER of 16.7% is obtained with the complex alternative compared to 16.9% for the real-valued one. In fact, both real and complex filters have the same frequency response in the positive domain. But using complex quadratic filters that produce analytic signal for which the complex Gabor filtered signal is an approximation could help for instantaneous frequency estimation [START_REF] Sommer | Geometric Computing with Clifford Algebras[END_REF] and preserves the phase information that can be useful for other tasks such as speaker recognition.

Then, Figure 3 illustrates the learnt cutoff frequencies. As expected, distributions are similar along a straight line for both models. In fact, both models roughly learn the same couples of cutoff frequencies due to an equivalent frequency response shape. Another drawback implied by Gaussian form functions could be the learning of large bandwidths. More precisely, the Gaussian shape is not ideal for large bandwidth filtering as depicted in figure 4. Indeed the frequency response tends to be flat in comparison to a rectangular filter. It is feasible to alleviate this issue by enabling the model to combine smaller band filters (Figure 4). However, and as expected, filters with larger bands are more distributed in the higher frequencies.

CONCLUSION

Summary. This paper introduces and releases a complexvalued and optimal time-frequency resolution alternative to the SincNet architecture. It is based on a complex Gabor filter learning process for automatic speech recognition. The conducted experiments show that the proposed approach is able to produce results comparable with state-of-the-art systems while operating on the raw waveform. Future Work. The base of the Gabor filters in non-orthogonal leading to redundancy in the filtered signals. It is therefore crucial to investigate other filters to produce an orthogonal base for better performances [START_REF] Mallat | A Wavelet Tour of Signal Processing: The Sparse Way[END_REF]. Furthermore, the interest of the phase still has to be established and this model must be evaluated on tasks relying on the phase and local information preserved by complex Gabor filters.

Fig. 1 :

 1 Fig. 1: Illustration of the real (g e ) and imaginary (g o ) parts of the complex Gabor filter impulse response.

with f 1 2 3

 12 and f 2 the low and high (-3dB) cutoff frequencies respectively, and A = 3ln(10) 10 a constant. The Gabor frequency response is depicted in Figure.

Fig.

  Fig. Illustration of the cutoff frequencies learnt with the Real and the Complex Gabor CNN.

Fig. 4 :

 4 Fig. 4: Illustration of a large band Gaussian filter. The top row shows how Gaussian filters can be flattened when the bandwidth is too large. The bottom row illustrates how smaller bandwidth Gaussian filters can be combined to obtain a better large band filter.

Table 1 :

 1 Results obtained with different ASR systems on the TIMIT phoneme recognition tasks. Valid. denotes the validation dataset, and CTC the Connectionist Temporal Classification training scheme. Results are expressed in Phoneme Error Rate (i.e. lower is better).

		Model	Valid.% Avg. Test% Best Test%
		Gabor-CNN-CTC [18]	-	18.8	18.5
		SincNet [2]	-	17.2	-
		GaborReal	15.2	17.2	16.9
		GaborComplex	15.2	17.1	16.7
	8,000	f 2
	6,000
	4,000
		Complex Gabor
	2,000	Real Gabor
		f 1
		1,000 2,000 3,000 4,000 5,000 6,000

https://github.com/NOEPG/pytorch-kaldi

This section details the proposed complex-valued model to directly operate of the raw speech waveform. First, SincNet is presented (Section 3.1). Then, we introduce the complex Gabor filtering alongside with the complex-valued architecture (Section 3.2).

ACKNOWLEDGEMENTS

This work was supported by the JST-ANR VoicePersonae Project and by the Engineering and Physical Sciences Research Council (EPSRC) under Grant: MOA (EP/S001530/).


Amandine Chevalier

Frédéric Lantz

Personal car, public transport and other alternatives? Predicting potential modal shifts from multinomial logit models and bootstrap confidence intervals

Keywords: Modal choice, personal car, public transport, shared car, multinomial logit model, conditional logit model, bootstrap confidence intervals

Households' daily mobility in France is characterized by the preponderance of the automobile. Passenger cars, mainly used by households but not only, are thus responsible for more than a half of fuel consumptions in road transport (CGDD/SOeS, July 2013) and more than a half of CO2 emissions in the transport sector (SOeS/CDC, December 2012). The main objective of this paper is thus to explain the modal choice of French households for their daily trips, particularly the importance of the car, and to predict potential shifts from personal car to public transport and other alternatives, especially shared car. An independent multinomial logit model is estimated and reveals the particular importance of car equipment on modal choices and specifically on car use. Predictions by 2020 are conducted according to three cases for the household's motorization (no car, one car, two cars or more) and per different mobility profiles. Personal car should remain the main mode of transportation by 2020 except if households have no car. In that case, modal shares would be more balanced, public transport would become the main transport mode and the shift to shared car would be at a maximum. Modal share of shared car could thus reach 16% for "exclusive motorists". A conditional logit model is also estimated and shows no particular importance of the means of transportation's costs in the modal choices. These results show that the increase in distances between 2010 and 2020 makes motorized modes more necessary. Thus, personal car and public transport should remain the main modes of transportation by 2020. Moreover, expected changes in costs and travel time by 2020 does not seem to have any effect on the deployment of shared car, its modal share being constant (in an average) between 2010 and 2020.

Introduction

Households' daily mobility in France is characterized by the preponderance of the automobile. Passenger cars, mainly used by households but not only, are thus responsible for more than a half of fuel consumptions in road transport (CGDD/SOeS, July 2013) and more than a half of CO2 emissions in the transport sector (SOeS/CDC, December 2012). But in recent years, we observe a decrease in fuel consumptions by private cars and an increase of fuel consumptions by motorcycles and buses and coaches (CPDP, 2012), suggesting a modal shift from private car to motorcycles and public transport. In the same time indeed, inflections in car use are observed. Thus, young people use less private car and are less often motorized than their elders. Moreover, households try to adapt to the high cost of car by travelling less kilometers by car each year, by pooling its use thanks to new mobility services such as carpooling and carsharing and by using more public transport in urban area. The new mobility services, especially carsharing, can be considered as empirical applications of the business model of the functional service economy. According to some researchers, the new business model consisting of the substitution of the sale of the product's function to the sale of its property, which is the concept behind the new individual mobility services we mentioned, allows for a decrease in production, lower consumption of natural resources, in addition to encouraging companies to design products that consume fewer resources in their production, use, maintenance, recycling and reuse [START_REF] Bourg | Des services aux entreprises à l'économie de la fonctionnalité : les enjeux du développement durable[END_REF][START_REF] Du Tertre | L'économie de fonctionnalité. Changer la consommation dans le sens du développement durable[END_REF]. [START_REF] Fourcroy | Functional service economy: a pathway to real energy savings? The case of vehicle rental by French households[END_REF] show that great energy savings can be achieved by these services only if they replace car ownership and do not add a new need of car. Moreover, compared to the use of private car by only one person, the use of public transport allows for a decrease in energy consumptions and CO2 emissions per capita. These are the reasons why the main objective of this paper is to explain the modal choice of French households for their daily trips, particularly the importance of the car, to predict potential shifts from personal car to alternatives such as public transport, motorcycle or shared car. From survey data (Mobility Observatory, BIPE, October 2010), we base on households' activities, ie their need for mobility, their car equipment, and socio-economic variables that could impact their modal choices. We estimate an independent multinomial logit model from these variables and a conditional logit model from characteristics of each mean of transportation (cost and travel time). From these estimations, we simulate modal choices by 2020 and apply a pairs bootstrap method to predict modal shares with confidence intervals. In a first part of the paper, we present a brief review of the literature. Then we describe the method and the data we use in this paper. Our results are then presented. The fourth section is devoted to the predictions of modal shares by 2020 and the last section to the discussion of our results.

Literature review

The decision of an individual among several unordered alternatives is generally modelled through multinomial logit models. As an example of such a decision, the choice between means of transport is modelled in this way. Modal choice models such as those estimated by [START_REF] Train | A validation test of a disaggregate mode choice model[END_REF], [START_REF] Carson | Experimental analysis of choice[END_REF] and more recently [START_REF] Hensher | Empirical approach to combining revealed and stated preference data: some recent developments with reference to urban mode choice[END_REF] are mainly built from quantitative data describing the characteristics of the various modes (costs, transfer or transport time, etc.). They can then be used to test the effects of a transport policy (construction of a new road, creation of a new line of transport, etc.). Thus, from a sample interviewed before the introduction of the Bay Area Rapid Transit (BART) in San Francisco in 1973[START_REF] Train | A validation test of a disaggregate mode choice model[END_REF] developed a model to measure the effect of the service in terms of modal split. From the same type of model, [START_REF] Carson | Experimental analysis of choice[END_REF] wanted to know how can change the modal share of the car if its cost increases. More generally, research on modal choices show that they are influenced by the level of service (travel time and cost differentials), but also by the characteristics of individuals and households, such as the level of income, car equipment, area of residence and place of work [START_REF] Stopher | Urban Transportation Modelling and Planning[END_REF][START_REF] Koppelman | Travel-choice Behavior: Models of Perceptions, Feelings, Preference, and Choice[END_REF][START_REF] Kanafani | Transportation Demand Analysis[END_REF][START_REF] Ben-Akiva | Discrete Choice Analysis: Theory and Application to Travel Demand[END_REF][START_REF] Wachs | Policy implications of recent behavioral research in transportation demand management[END_REF]. Moreover, the choice of a mode of transportation can be studied for a particular type of trip, most often commuting. This is particularly what study [START_REF] Train | A validation test of a disaggregate mode choice model[END_REF] in San Francisco, [START_REF] Hensher | Empirical approach to combining revealed and stated preference data: some recent developments with reference to urban mode choice[END_REF] in six Australian cities, Liu (2007) in Shanghai, Khattak and Palma in Brussels (1997). Some are also interested in the impact of unexpected events on the modal choice. Thus, Khattak and[START_REF] Khattak | Stated and Reported Diversion to Public Transportation under Incident Conditions: Implications on the Benefits of Multimodal ATIS, Partners in Advanced Transit and Highways[END_REF][START_REF] Khattak | Commuters' normal and shift decisions in unexpected congestion: Pre-trip response to advanced traveler information systems[END_REF] show that longer travel time on road may encourage motorists to use public transport. Moreover, [START_REF] Khattak | The impact of adverse weather conditions on the propensity to change travel decisions: a survey of Brussels commuters[END_REF] show that adverse weather conditions encourage half of motorists in Brussels to change their departure time or their itinerary. It can also be question of interdependence between the choice of transport mode and trip purpose, more precisely the organization of trips depending on the schedule of the day. Thus one part of the literature focuses on modal choices on the basis of household's activities (activity-based demand model). [START_REF] Damm | Theory and empirical results: a comparison of recent activity-based research[END_REF], [START_REF] Golob | A classification of approaches to travel-behavior analysis[END_REF], [START_REF] Kitamura | An evaluation of activity-based travel analysis[END_REF] and Etterna (1996) conduct literature reviews on this subject. We mainly retain that [START_REF] Pas | The effect of selected socio-demographic characteristics on daily travel-activity behaviour[END_REF] shows that demographic factors such as employment status, gender, or the presence of children in the household have a significant impact on the activities and trips. In addition, [START_REF] Kitamura | Incorporating trip chaining into analysis of destination choice[END_REF] identifies the interdependence between the choice of destinations in travel chains and the choice of the mode of transportation. Moreover, [START_REF] Bhat | A conceptual framework of individual activity program generation[END_REF] propose an analytical model based on the organization of activities. More specifically and always on the basis of households' activities, the first models of travel chains were mainly developed in the 70's and 80's in the Netherlands [START_REF] Daly | Application of disaggregate models for a regional transport study in The Netherlands[END_REF][START_REF] Gunn | Long range country-wide travel demand forecasts from models of individual choice[END_REF]Hague Consulting Group, 1992;[START_REF] Gunn | The Netherlands National Model: a review of seven years of application[END_REF]. They were then used to model the movements in different cities and countries: Stockholm [START_REF] Algers | Stockholm model system (SIMS): application[END_REF], Salerno, Italy [START_REF] Cascetta | A system of mathematical models for the evaluation of integrated trac planning and control policies[END_REF], Boise, Idaho [START_REF] Shiftan | A practical approach to incorporate trip chaining in urban travel models[END_REF], New Hampshire [START_REF] Rossi | Tour Based Travel Demand Modeling in the US[END_REF] or Boston [START_REF] Bowman | Activity-based disaggregate travel demand model system with activity schedule[END_REF]. A key finding highlighted by [START_REF] Krygsman | Capturing tour mode and activity choice interdependencies: A co-evolutionaly logit modelling approach[END_REF] is that there are variations in the order of choice of travel mode and trip purpose. But in most cases, the travel pattern is done before the modal choice. This therefore indicates that it rather depends on the choice of the pattern and the travel chain considered. It is precisely on this need for mobility we base to try to explain the modal choice, as well as on variables describing individuals and households and variables that are characteristics of the different modal choices (travel costs and time).

Methodology and data

As described in the introduction, the decrease in fuel consumptions by private cars and the increase of fuel consumptions by motorcycles and buses and coaches observed in recent years (figure 1), suggest a modal shift from private cars to motorcycles and public transport. Moreover, we observe a shared use of the car especially through carpooling and carsharing. Thus we decide to explain the modal choice of French households to predict potential shifts from personal cars to alternatives such as public transport, motorcycles or shared cars by 2020. The transport mode's choice is based on several factors corresponding to the travel mode's (distance, time, etc.) and to the household's characteristics. As mentioned in the previous section, there is a large literature on this topic. Each study point out that the choices are related to the characteristics of a country at a given period. A classical way to assess these choices is to use a multinomial logit model which aims to explain the modal choices by a set of explanatory factors. In the next two paragraphs, we develop the econometric approach that we use for the models' estimations and forecasts. Then, we present the data which are considered for the statistical estimation.

Multinomial logit model

The objective of the model is to explain that each individual i (i,=1,…n) has a choice between a set of unordered alternatives j (j=0,…m). Here, we consider m+1=6 alternative transportation's modes. As this dependent variable is a qualitative one with a limited number of unordered terms, we use a discrete choice model: the multinomial logit model (MLN). More specifically, we use two types of logit models: single or independent multinomial and conditional. The distinction between these two types of models is primarily based on the nature of the selected explanatory variables. The first includes variables that are characteristics of individuals, while the second includes variables that are characteristics of the different means of transportation and differ according to the dependent variables and individuals as well. In the case of modal choice, individual i compares the different levels of utility associated with different choices and chooses the one that maximizes his utility from the j choices. For individual i, the utility of the choice j is:

Uij =f ( β Xij) + εij (1)
Where β is a vector of unknown parameters, Xij is a vector of the individuals' or households' characteristics and εij a random error term.

As MLN are probabilistic models, their results reflect the utility maximization. Thus the probability that the individual i chooses the alternative j is the probability that the value of j is greater than that associated with all other modes. For instance, for j=0:

Prob(yi=0)=Prob (Ui0 > Ui1, Ui0 > Ui2,… Ui0 > Uim ) (2)
We denote Uij = Vij + εij where Vij is a deterministic function and εij a random variable.

Thus, the probability that the individual i chooses the alternative 0 is:

Prob(yi=0) = 𝑒 𝑣𝑖𝑗 ∑ 𝑒 𝑣𝑖𝑘 𝑚 𝑘=1
(3)

As Vij = xiβj, in the case of an independent logit model, then the probability that the individual i chooses the alternative j is:

Prob(yi=0) = 𝑒 𝑥𝑖𝛽𝑗 1+ ∑ 𝑒 𝑥𝑖𝛽𝑘 𝑚 𝑘=1 (4)
As Vij = xijβ, in the case of a conditional logit model, then the probability that the individual i chooses the alternative j is:

Prob(yi=0) = 𝑒 𝛽𝑧 * 𝑖𝑗 1+ ∑ 𝑒 𝛽𝑧 * 𝑖𝑘 𝑚 𝑘=1 (5)
Where z*i,j = xi,kxi,0

The parameters' estimations are obtained by the method of maximizing the log likelihood of the model with constants using the SAS software version 9.4 through Logistic and Mdc procedures.

Bootstrap prediction intervals

The estimated multinomial logit models are then used for predictions. For this purpose, we consider a set of expected future values of the explanatory variables Xf from which we predict the probability of each transportation's mode Prob(y f =j).

From logit model, it is only possible to perform predictions for ''case study'' i.e. for a new individual representative of the population in 2020. Thus, we set the main explanatory variables according to their most probable evolution by 2020 in an average. However, the probability distribution being not linear, the average probabilities predicted by the models are not equal to the probability at the average of the variables as shown in figure 2. It is therefore imperative to provide predictions with confidence intervals. To do this, we use the method of bootstrap prediction intervals. The principle of the bootstrap is to approximate the theoretical distribution of a statistic of interest from the empirical distribution obtained from B random samples of size N in the sample of the original data. In our case, we repeat B=1,000 times a random drawing with replacement of 1,413 individuals of the original population with their characteristics (pairs bootstrap) to get 1,000 bootstrap samples. We then estimate the models on each of the 1,000 samples to obtain an empirical distribution of the probabilities predicted by the models.

From these distributions we construct confidence intervals with 95% degree of confidence. The bootstrap method is realized using the SAS software version 9.4 through the surveyselect procedure.

Data and economic analysis

As described in the literature review, modal choices are associated with travel needs corresponding to the distance to travel for different purposes, individuals' characteristics, and travel cost and time. The assessment of these choices depends therefore on individual data based on surveys. In our case, we base on a sample of 1,413 people (representative of the French population) involved in the Mobility Observatory (BIPE, October 2010). This survey is conducted every six months to describe mobility practices of French households. The questionnaire is passed face to face during 45 minutes to one hour. For this work, we take into account three main questions concerning the travel modes used for a "normal week day", the transportation mode used for the different mobility patterns and the distance travelled with each of the different travel mode. Thus we define travel needs as the distance to travel for each of the mobility purpose.

The variable to explain is the modal choice on a normal week day. We take into account the primary mode of transportation that is the one with which individual travel the highest distance each day. It has six categories: personal car (including company car), shared car (carpooling and carsharing), motorcycle, bike, walking and public transport. The modal distribution of the sample is described in figure 3. 59% of individuals use personal car which is the main mode of transportation to travel each day. Thus 84% of daily kilometres are travelled by personal car.

The second mode is public transport used by 20% of the sample to travel 12% of the travel needs each day, followed by walking for 15%. Shared car is used by only 1% (homogeneous groups of people for carpooling and carsharing) to travel less than 1% of the daily travel needs.

In a preliminary work on the same data set we performed a multiple correspondence analysis from the main individuals' socio-economic and travel characteristics (see table 1 in appendix). It shows that the most discriminating variables distinguishing mobility profiles are: the travel need, i.e. the distance to travel (in km / pattern), the type of the municipality of residence (density), the marital status, the household's motorization, the age, the employment status and the income. Thus we use these variables to estimate multinomial logit models to explain modal choice. Moreover, this work led to the construction of mobility profiles described in figure 4. The first level of partition distinguishes "exclusive motorists" from others. These individuals have the highest travel needs for all patterns and move exclusively by car. They are from 30 to 60, are working, live in couple and have children. They live in low density areas and are motorized. The rest of the population is then cut in two classes: people using their car (exclusively or in combination with one or more other modes) and people being "multimodal". The third level of partition occurs between individuals using the car (the "motorists"), some travelling on low distances, others having higher travel needs and living in lower density areas. Within the group of "multimodal" we then distinguish people living alone (rather non-working or workers, under 30 or over 60, without children, with modest incomes, living in large city-center, non-motorized and travelling mainly by motorcycle, walking and public transport), from people living in family (with two working persons, under 60, with children, living in Paris area and large city-center, motorized and travelling mainly by car, motorcycle, walking or public transport). Within the "singles" we distinguish "pensioners" of more than 60, living alone and walking or using public transport, from "young" inactive or low-skilled labour, living alone or with roommates, and travelling mainly by motorcycle, walking or public transport. Finally, within the "families" we distinguish "working couples" of more than 30 and travelling mainly by car, from "students" of less than 30 travelling mainly by motorcycle, walking or public transport.

Finally we select the following explanatory variables to explain modal choices for daily trips: the travel need which corresponds to the distance to travel for different purposes and is linked to the density of the municipality of residence (from 1=Paris to 7=rural area), the household's motorization (0 car, 1 car, 2 cars or more) which is linked to the household's income, the marital status (single, couples, cohabitation / roommate) and the age linked to the employment status (0=not working, 1= working). In addition, it is possible to model modal choices from their own characteristics: their costs and travel time. The expenditure incurred by the travellers to the use of public transport in France was calculated by the National Federation of Transport Users (FNAUT, 2012) and corresponds to the price paid by users for public transport thus taking into account state aids. The costs of personal car and motorcycle correspond to the mileage rates set by the French tax administration. The cost of shared car is a half of that of the private car.

The travel time with each mode of transport is also taken into account to explain modal choice. It is calculated from the distance to travel and the average speed associated with each of the transportation mode (the average speed is that observed in the Mobility Observatory in October 2010).

Results

From the different characteristics we thus estimate two types of logit models: an independent model from individuals' characteristics and a conditional model from the travel modes' characteristics.

Independent logit model

Estimated parameters

We estimate an independent multinomial logit model explaining the modal choice between six different modes (personal car, shared car, motorcycle, bike, walking and public transport) by the explanatory variables distance to travel, density of the municipality of residence, household's motorization, age, marital status, employment status and income. The distance is the log of the kilometers travelled each day with the primary transportation mode, the density of the municipality of residence is a density index going from 1 for Paris to 7 for the rural area, the household's motorization corresponds to three cases: the household has no car, one car, or two cars or more, the marital status as well: single, in couple, or in cohabitation, and the employment status is a binary variable: 0 if the person is not working and 1 if the person is working.

Quality indicators of the model are good enough (ρ² McFadden: 0.58 and Estrella indicator: 0.95), but the estimators associated with activity status and income are not significant so we cannot say that they have an effect on the modal split in the sample we study. This conclusion cannot be generalized to the total population in that the significance of the parameters depends on the sample size. We decide anyway to remove the employment status and income variables, which does not deteriorate the quality of the model in so far as the employment status is clearly correlated to the age and the income to the household's motorization. This one is therefore an indicator of standard of living. The model is estimated with the personal car as the reference.

Table 1 shows that the distance has a negative effect on the use of alternatives to the personal car: the longer the distance to travel, the greater the probability to choose the personal car. Similarly, the lower the density of the residence area, the higher the household is motorized, the older the person and the more there are people in the household, and the more the alternatives to the car are used. Only variables of motorization and marital status appear to have an effect on the choice between personal and shared car. Obviously, non-motorized people have no choice than using shared car. Contrary to intuition, age does not seem to have any effect on the choice between personal car and shared car. In addition, motorization seems to be crucial. However, it is important to remain vigilant with these findings in that, on the observed sample, we have very few individuals using shared car.

Odds ratio

The interpretation of estimated parameters can be specified by measuring the magnitude of a change in explanatory variables on the probability to use each mode of transportation through odds ratio presented in table 2. Odds ratios are calculated as follows: Increasing the distance to travel of one unit decreases the probability of using alternative modes to personal car of 0.23 points (1-0.769) for shared car, 0.46 points for motorcycle, 0.84 points for bike, 0.90 points for walking and 0.52 points for public transport. Concerning shared car, this result shows that for a given level of distance to travel, it is better to own a private car than sharing a car when needed so that individuals are quite rational.

Odds ratio kj = exp [βkj] (6)
Similarly, the decrease in the density of the residential area decreases the same probability from 0.38 points for public transport to 0.19 for walking, but increases the probability to use shared car, which means that it should rather develop in low density areas. But we must be careful with this conclusion which is mainly explained by the fact that shared car is mainly used in the less dense area in our sample.

To be older of one year also decreases this probability: from 0.07 points for motorcycle to 0.01 points for shared car.

An extra car owned by the household also decreases this probability: from 0.98 points for motorcycle to 0.81 points for walking. The motorization is crucial: its effect on the probability of choosing the different modes of transportation is the largest. Once purchased, the car is thus used almost exclusively. This conclusion has been already widely demonstrated in the literature. Finally, with an additional person in the household, it is 1.9 times more likely to choose walking than personal car or 3.24 times more likely to choose motorcycle. Thus, the more in the household (even if it is motorized), the less likely to use the personal car.

Independence of Irrelevant Alternatives (IIA) assumption test

To test the independence of irrelevant alternatives assumption necessary to validate the multinomial logit model, we realize the test proposed by [START_REF] Hausman | Specification Tests for the Multinomial Logit Model[END_REF]. Thus, we calculate the test statistic S for five different sub-groups in which we removed each time a modality (except personal car which is the reference category). Thus we consider A1 the sub-group excluding shared car, A2 excluding motorcycle, A3 excluding bike, A4 excluding walking and A5 excluding public transport.

As shown by [START_REF] Hausman | Specification Tests for the Multinomial Logit Model[END_REF], the test statistic can be negative, especially in the case of small samples. This does not then challenge the IIA property. As shown in table 3, in the case of subgroups excluding motorcycle, walking and public transport, the test statistic S follows a 𝜒² distribution with 24 degrees of freedom.

In the subgroup excluding motorcycle, the test statistic is less than the critical value (at 99.5%) so we do not reject H0. P-value = 1 also tells us that there are 100% chance of being wrong in rejecting the null hypothesis of independence. The IIA assumption is indeed satisfied in this case. Similarly, in the subgroup excluding walking, the test statistic is less than the critical value (at 99.5%) so we do not reject H0, p-value = 0.99 also indicates that there are 99% chance of being wrong in rejecting the null hypothesis of independence. Finally, in the subgroup excluding public transport, p-value = 0.87 indicates that there are 87% chance of being wrong in rejecting the null hypothesis. Thus we do not reject the null hypothesis at 87% and have 13% chance that our model does not respect this property.

Conditional logit model

To take into account the economic rationality of individuals in their modal choices, we estimate a conditional logit model, taking into account variables that are characteristics of choices: the cost and travel time. In addition, we also introduce specific constants for each mode of transport to take into account their own characteristics hardly captured elsewhere (including comfort for example). Table 4 shows that parameters associated with the constants are all negative which confirms the preference for personal car compared to all other means of transportation for its comfort, flexibility… In addition, the parameters associated with the cost and travel time are negative which means that a high cost and a long travel time do not encourage the use of alternative modes to the personal car. This result shows that mobility is an arbitrable need on the basis of its cost. Thus, odds ratios show that an increase in the cost of a transport mode (of a cent per kilometer) decreases by 0.02 points the probability of its use (1-0998). Similarly, an increase in the travel time of one minute of a mode of transport decreases by 0.06 points the probability of its use.

The model is estimated with the personal car as the reference.

Predictions by 2020 and bootstrap prediction intervals

The objective of the predictions is to predict the modal choices in 2020 from the estimated models. Thus we set the main explanatory variables according to their most probable evolution, in an average, by 2020 to try to approach the closest to reality.

Independent logit model

Hypothesis

The independent logit model explaining modal choices is estimated using the following variables: the distance, the category of the municipality of residence (density), age, motorization and marital status. About the distance to travel, we base on figures from the National Transportation Survey (INSEE, 1982;[START_REF] Centre | Transports et communications[END_REF][START_REF] Soes | Transports et déplacements (ENTD)[END_REF] to realize a projection to 2020 based on a logarithmic adjustment on previous data and continuing the observed trend. Indeed, according to a recent report to the French Minister of Transport by the Commission "Mobilité 21" ( 2013), travel need should grow by 2020 but its growth should be weaker than in the past. These evolutions are applied to the data in our sample. Therefore, the log of the distance to travel in 2010 was 3.029 and will be 3.102 in 2020. This result is that applying on an average of the sample, but the trend between 2010 and 2020 is applied to the average distances observed in each subgroup used to perform predictions (different mobility profiles) and that is the case for all other explanatory variables.

In our sample, the mean age is 47.2 years in 2010. According to population's projections made by the BIPE (Residential Migration, 2010), the average age is expected to increase in 2020 and should be 48.7 years.

In our sample, people living in a couple are the majority. According to the BIPE's projections (Residential Migration, 2010), this mode of cohabitation should remain dominant in 2020 but the number of households of one person is expected to grow: singles will be 45% of the households in 2020 (42% in 2010) and couples will be 52% (55% in 2010).

Concerning the evolution of the distribution of households between urban and rural areas, projections of the BIPE (Residential Migration, 2010) show no significant changes by 2020. Therefore, we do not change the structure depending on the category of municipality of residence. Finally, as motorization is a key explanatory variable of modal choice, we perform predictions in three cases: the household has no car, the household has one car (current situation on average and therefore central scenario) and the household has two cars or more.

Predictions and bootstrap confidence intervals

To obtain results close from reality, we realize our forecasts according to the different mobility profiles presented in section 2.3 (figure 3). From the logit model we obtain the choice probability of the average individual representative of each profile. Moreover, we consider three sets of values for explanatory variables according to the households' motorization (no car, one car, two cars or more).

Substitutions between travel modes

From bootstrap replications, we obtain statistical distributions of probabilities predicted by the independent model. In the case where the household has no car, we study potential modal shifts from personal car to public transport, motorcycle and shared car by distinguishing the probabilities to use them depending on whether we are above or below the median of the probability of using private car. As shown by figures 6, 7 and 8, the people using the less personal car (the 50% using personal car the less) are more among those using public transport, motorcycle and shared car the most. Thus we observe a potential modal shift from personal car to public transport, motorcycle or shared car.

Conditional logit model

Hypothesis

The conditional model is estimated from the variables of cost and travel time.

Concerning transportation costs, we base on the calculation of expenses incurred by the travellers by car and public transport between 1970 and 2010 conducted by the National Federation of Transport Users (2012). In 2020, these costs correspond to the projection of the linear fit of the observed costs between 1970 and 2010. This evolution is then applied to the cost of other modes of transportation (shared car and motorcycle). The transportation costs to 2020 will therefore continue to increase.

In addition, we propose a scenario in which we apply a carbon tax. Indeed, at the environmental conference on 20 and 21 September 2013, the entry into force of a Climate-Energy Contribution (CEC) in 2014 was announced (Le Figaro, September 20 th , 2013). The price of a ton of carbon is 7 € in 2014 and then increases to 14.5€ in 2015 and 22 € in 2016. In 2020, we retain a CO2 price at 22 € / ton. At this price, the impact of the tax on the user cost per kilometer of the car or motorcycle is almost zero (0.4 € cents / km). We also apply very high taxes but no inflection in use behaviour of different modes of transport is observed. Finally, the transport time to 2020 depends on the evolution of distances whose assumptions were presented in section 4.1.1, the speed remaining constant. Therefore, the average transport time will increase by 6% by car and motorcycle, 6.7% by bike, 7.6% by walking and 8.1% by public transport.

Predictions and bootstrap confidence intervals

The predictions are performed at the average point of the sample and give the modal distribution shown in figure 9. These results show that the increase in distances between 2010 and 2020 makes motorized modes more necessary. Thus, personal car and public transport should remain the main modes of transportation by 2020. In addition, costs of the different means of transport increasing linearly, differentials of cost do not vary. Arbitrations are thus rather realised in terms of travel time than costs.

Concerning shard car more precisely, expected changes in costs and travel time by 2020 does not seem to have any effect on its deployment, its modal share being constant (in an average) between 2010 and 2020. It will be 1.21% at a maximum as shown in table 7.

Predictions have also been realized taking into account a carbon tax. At different prices of the carbon tax (from 22€/ton to very high taxes), costs do not really differ from the situation without a carbon tax and no modal shift is observed. Moreover, even if the car costs are doubled, we do not observe modal shifts or a significant increase in the use of shared car. [57,25 ; 67,25] [0,45 ; 1,21] [1,87 ; 3,34] [2,57 ; 4,15] [0,39 ; 15,39] [19,00 ; 26,18]

Substitutions between travel modes

From bootstrap replications, we obtain statistical distributions of probabilities predicted by the conditional model. Thus we study potential modal shifts from personal car to public transport, motorcycle and shared car with the same method than in the section 4.1.3. As shown by figures 10, 11 and 12, the people using the less personal car use public transport and motorcycle the less too and shared car the most. From rational considerations, we observe less modal shifts from personal car to public transport or motorcycle but rather to shared car.

Discussion

Firstly, conclusions have to be taken with caution, especially for shared car, because we do not dispose of a large sample to analyze travel behavior and there are few observations concerning the use of shared car for daily trips. From the independent logit model, predictions by 2020 have been conducted by mobility profiles to reflect the diversity of mobility habits. However, application of these mobility profiles to the conditional logit model does not allow assessing correctly the modal distribution observed in 2010. As a consequence, predictions from the conditional logit model have been performed at the average point. That means that, apart from purely rational considerations (cost and time of transport), modal choices are driven by other factors that are characteristics of households and their travel needs. Those two approaches are thus complementary and show that personal car should remain the main mean of transportation by 2020 with public transport. Predictions by 2020 have been performed according to three cases of household's motorization from the independent logit model. We show that the use of personal car could decrease only if household's motorization decreases. In that case public transport would become the main mode of transportation and shared car would develop. But this situation of household's de-motorization is obviously not possible by 2020. However, changes in households' motorization are observed and it will be determinant to work on the future of households' motorization to know precisely its future level. Moreover, we notice that, even for a household with no car, modal share of personal car is not zero. This is explained by the fact that we introduce company car as a personal car in so far the household has it at its disposal as a private car owned by the household. In 2010, 2.6% of the sample use company car as a daily travel mode. The predictions results by 2020 show that personal car's share could reach 20% in the case of not motorized households. That means that there always will be a need of car available to households but that the mode of holding will change: the car will not necessarily owned by the household. Thus personal car and public transport should remain the main modes of transportation by 2020, which implies that the supply of them should be available and sufficient everywhere.

In addition, forecasts from the conditional logit model could be achieved by income deciles to highlight the weight of the transport budget (as shown by [START_REF] Merceron | Les dépenses d'énergie des ménages depuis 20 ans : une part en moyenne stable dans le budget, des inégalités acccrues[END_REF] and the implications of a potential carbon tax on households more or less wealthy and dependent on their car that is hidden by the prediction from a midpoint. Finally, methods used in this paper to measure the potential development of shared cars in daily trips do not take into account diffusion phenomena or learning effects. Predictions realized in this paper are thus floor values for the use of shared car by 2020.

Conclusion

This paper shows that the main drivers of modal choices are the distance to travel, the density, the age, the marital status, the household's motorization, and travel cost and time. In an independent multinomial logit model, we confirm that motorization is the most determining factor of modal choices of French households in general and car use in particular. Thus the results of predictions by 2020 show a wide variation depending on the motorization scenario. In addition, the longer the distance to travel, the more we use motorized modes. However, an increase in the distance to travel results in a decrease of the probability to use shared car. This probably means that people with the highest needs to travel are motorized (what is then more profitable than carsharing) and suggests that shared car can hardly become a mean of transportation used exclusively. Thus the predictions show that personal car should remain the main mode of transportation by 2020, except if households have no car, which is the only case in which shared car could deploy, but in which public transport would become the main mode of transportation with personal car and motorcycle. Moreover, the study of statistical distributions of predicted probabilities for public transport, motorcycles and shared cars shows a substitution from personal car to these alternative travel modes. Furthermore, "motorists" are the main target for shared car, which means that we could observe shift from personal to shared car. But "motorists" are also those with the highest travel needs and the most motorized.

In addition, the estimation of a conditional logit model based on variables characteristics of the different modes of transportation (travel cost and time) shows that economic rationality explains modal choices as well and that the two approaches are complementary. Moreover, the increase in distances between 2010 and 2020 makes motorized modes more necessary. Thus, personal car and public transport should remain the main modes of transportation by 2020. Furthermore, only very high values of carbon tax could influence modal choices. However, expected changes in costs and travel time by 2020 does not seem to have any effect on the deployment of shared car, its modal share being constant (in an average) between 2010 and 2020. It could be 1.21% at a maximum. But from rational considerations, we observe less potential modal shifts from personal car to public transport and motorcycles but rather to shared cars. Therefore, the use of shared car seems to correspond to a specific profile and be essentially driven by the motorization of the households (as for all other travel modes). But the relationship between motorization and shared car use is not very simple and the de-motorization of households is not really possible by 2020, that is the reason why it will be determinant to work on the future of households' motorization and to connect the results with the predictions realized in this paper The "Cahiers de l'Économie" Series

The "Cahiers de l'économie" Series of occasional papers was launched in 1990 with the aim to enable scholars, researchers and practitioners to share important ideas with a broad audience of stakeholders including, academics, government departments, regulators, policy organisations and energy companies.

Figure 1 -

 1 Figure 1 -Fuel consumption in France (a) in 2000 and (b) 2011, from CPDP (2012)

Figure 2 -

 2 Figure 2 -Theoretical probability distribution of predicted probabilities

Figure 3 -

 3 Figure 3 -Modal distribution of the sample (a) among individuals and (b) passenger-kilometers (Mobility Observatory, BIPE, October, 2010)

Figure 5 -

 5 Figure 5 -Modal shares in France in 2010 and 2020 according to three cases of motorization

Figure 6 -Figure 8 -

 68 Figure 6 -Statistical distribution of predicted probabilities for public transport by 2020

Figure 9 -

 9 Figure 9 -Modal shares in France in 2010 and 2020

Figure 11 -

 11 Figure 11 -Statistical distribution of predicted probabilities for motorcycle by 2020

  However, this is the only French survey representative of the French population and taking into account shared daily travel mode. The Household Travel Surveys only concern urban areas and the National Transportation Survey does not take into account shared car (carpooling and carsharing) as a daily travel mode.

Table 1 -

 1 Estimated parameters

	Variable	Shared car	Motorcycle	Bike	Walking	Public transport
	Constant	-3.8070**	3.6326***	6.1623***	5.8934***	4.5689***
		(1.9152)	(1.0709)	(0.9501)	(0.6520)	(0.5291)
	Distance	-0.2625	-0.6165***	-1.8559***	-2.3348***	-0.7297***
		(0.2946)	(0.2174)	(0.2151)	(0.1451)	(0.0920)
	Density index	0.3062	-0.2449**	-0.2455**	-0.2080***	-0.4802***
		(0.1879)	(0.1145)	(0.1059)	(0.0655)	(0.0544)
	Motorization	-2.6028***	-3.8533***	-3.0637***	-1.6787***	-2.0262***
		(0.5760)	(0.4233)	(0.3527)	(0.2157)	(0.1811)
	Age	-0.0107	-0.0722***	-0.0519***	-0.0121*	-0.0233***
		(0.0170)	(0.0140)	(0.0102)	(0.006302)	(0.005149)
	Marital status	1.1477**	1.1749***	0.8464***	0.6427***	0.8741***
		(0.5057)	(0.2767)	(0.2909)	(0.2084)	(0.1534)
	Number of obs.			1413
	Log-likelihood			-1079
	Standard deviation in parenthesis

***: significant at 1% ; **: significant at 5% ; *: significant at 10%

Table 2 -

 2 Odds ratio

	Variable	Shared car	Motorcycle	Bike	Walking	Public transport
	Distance	0.769	0.540	0.156	0.097	0.482
	Density index	1.358	0.783	0.782	0.812	0.619
	Motorization	0.074	0.021	0.047	0.187	0.132
	Age	0.989	0.930	0.949	0.988	0.977
	Marital status	3.151	3.238	2.331	1.902	2.397

Table 3 -

 3 Results of the IIA assumption test

		S	p-value
	A1 : shared car excluded	Negative
	A2 : motorcycle excluded	2.6645332	1.00
	A3 : bike excluded	Negative
	A4 : walking excluded	6.0857236	0.99
	A5 : public transport excluded	16.570484	0.87

Table 4 -

 4 Conditional logit model: estimated parameters and odds ratio

	Variable	Estimated parameters	Odds ratio
	Cs_shared car	-4.2787*** (0.2931)	0.014
	Cs_motorcycle	-3.1629*** (0.1711)	0.042
	Cs_bike	-2.6704*** (0.1585)	0.069
	Cs_walking	-0.4331*** (0.1155)	0.649
	Cs-public transport	-0.9830*** (0.0710)	0.374
	Cost	-0.0016** (0.0008)	0.998
	Travel time	-0.0055*** (0.0007)	0.994
	Number of observations	1414
	Log-likelihood	-1573
	ρ² McFadden	37.89
	Estrella indicator	81.57
	Standard deviation in parenthesis
	***: significant at 1% ; **: significant at 5% ; *: significant at 10%

Table 7 -

 7 Modal shares in France and bootstrap confidence intervals in 2010 and 2020

	Year	Personal car	Shared car	Motorcycle	Bike	Walking	Public
							transport
	2010	58,7%	0,8%	2,5%	3,1%	15,0%	20,0%
	2020	60,0%	0,8%	2,6%	3,4%	12,1%	21,2%
	Bootstrap CI

I. CADORET, J.-L. KARNIK

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	# 24. D. BABUSIAUX, J. JAYLET* All these papers are available upon request at IFP School. All the papers issued after 2004 can be Calculs de rentabilité et mode de financement des downloaded at: www.ifpen.fr investissements, vers une nouvelle méthode ?
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		Mars 1991 externes liés à la pollution automobile : difficultés	l'industrie ; méthodes et interrogations pour
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		Élasticités et substitutions énergétiques : difficultés
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			et en Europe : comparaison et interdépendance.
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E-mail address: amandine.chevalier@ifpen.fr

Acknowledgment

The authors would like to thanks particularly Leopold Simar, Fanny Rougier, Hugo Delavaquerie and Simon Michaut for their help at different steps of this work.

The aggregated results correspond to the weighted sum of the average individual forecasts for each mobility profile as recommended by [START_REF] Ben-Akiva | Discrete Choice Analysis: Theory and Application to Travel Demand[END_REF]. They provide the modal split described in the figure 5.

In the original sample, 18% of households are not motorized, 62% have one car and 20% have two cars or more. The results show a wide variation depending on the motorization scenario. Personal car should remain the main mode of transportation by 2020 except if households have no car. In that case, public transport would become the main mode of transportation, the modal distribution would be more balanced and shared car would deploy. More specifically, these general conclusions should be specified by discussing the results per mobility profile.

We choose to provide the detailed results of two extreme profiles, the others being just discussed. The "pensioners walking and using public transport" mainly includes people with no car. That is why we study only one alternative: the equipment (one car), as shown in table 5. In this case, the probability of using the private car increases while that of all other modes decreases. Being by nature not very motorists "pensioners walking and public transport" do not constitute an important target for car-sharing: 2.37% at a maximum as shown by bootstrap confidence intervals. [12.53 ; 20.94] [0.19 ; 2.37] [0.53 ; 2.8] [3.75 ; 10.7] [35.82 ; 50.1] [24.89 ; 37.66] Similarly "young alternative to car" use less car (personal and shared) than the average population and more motorcycle, bike and public transport. They are mainly motorized (one car). The shared car could only grow in the case of a household with no car to 3.93% at a maximum. "Working and motorist couples" however use more personal car than the average population and are an attractive target for car-sharing, especially in the case of a household without a car. In that scenario the use of public transport could also develop significantly, especially since they mainly live in urban areas (Paris and its region and city centers of more than 100,000 inhabitants). "Students alternative to car" mainly use public transport and motorcycle. They are also the second shared car users.

But their low car use (personal as shared) does not make them a prime target for shared car. Thus, a decrease in the use of personal car is accompanied by an increase of motorcycle, bike and walking. "Motorists" on the contrary use more personal car than the average population. The more their travel needs are important, the more they use it. They are preferred targets for car-sharing, but also for motorcycle and public transport, primarily in a scenario of a household not motorized.