Biogeme & Binary Logit Model Estimation
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1 Biogeme & Binary Logit Model Estimation Anna Fernández Antolín Transport and Mobility Laboratory School of Architecture, Civil and Environmental Engineering École Polytechnique Fédérale de Lausanne April 26, 2016 AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
2 Today Further introduction to BIOGEME Estimation of Binary Logit models AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
3 How does BIOGEME work? model.mod data.dat BIOGEME Results.html Final model.res parameters default.par Data statistics etc..sta.log.rep... AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
4 BIOGEME - Data file File extension.dat First row contains column (variable) names. One observation per row. Each row must contain a choice indicator. Example with the Netherlands transportation mode choice data: choice between car and train. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
5 BIOGEME - Data file netherlands.dat id choice rail_cost rail_time car_cost car_time AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
6 BIOGEME - Data file netherlands.dat id choice rail_cost rail_time car_cost car_time Unique identifier of observations AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
7 BIOGEME - Data file netherlands.dat id choice rail_cost rail_time car_cost car_time Choice indicator, 0: car and 1: train AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
8 BIOGEME - Model file File extension.mod Must be consistent with data file. Contains deterministic utility specifications, model type etc. The model file contains different [Sections] describing different elements of the model specification. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
9 BIOGEME - Model file How can we write the following deterministic utility functions in BIOGEME? V car = ASC car +β time time car +β cost cost car V rail = β time time rail +β cost cost rail AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
10 BIOGEME - Model file [Choice] choice [Beta] // Name DefaultValue LowerBound UpperBound status ASC_CAR ASC_RAIL BETA_COST BETA_TIME [Utilities] //Id Name Avail linear-in-parameter expression 0 Car one ASC_CAR * one + BETA_COST * car_cost + BETA_TIME * car_time 1 Rail one ASC_RAIL * one + BETA_COST * rail_cost + BETA_TIME * rail_time AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
11 BIOGEME - Model file [Choice] choice [Beta] // Name DefaultValue LowerBound UpperBound status ASC_CAR ASC_RAIL BETA_COST BETA_TIME [Utilities] //Id Name Avail linear-in-parameter expression 0 Car one ASC_CAR * one + BETA_COST * car_cost + BETA_TIME * car_time 1 Rail one ASC_RAIL * one + BETA_COST * rail_cost + BETA_TIME * rail_time AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
12 BIOGEME - Model file [Choice] choice [Beta] // Name DefaultValue LowerBound UpperBound status ASC_CAR ASC_RAIL BETA_COST BETA_TIME [Utilities] //Id Name Avail linear-in-parameter expression 0 Car one ASC_CAR * one + BETA_COST * car_cost + BETA_TIME * car_time 1 Rail one ASC_RAIL * one + BETA_COST * rail_cost + BETA_TIME * rail_time AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
13 BIOGEME - Model file [Choice] choice What is one? [Beta] // Name Which is the type of model? DefaultValue LowerBound UpperBound status ASC_CAR ASC_RAIL BETA_COST BETA_TIME [Utilities] //Id Name Avail linear-in-parameter expression 0 Car one ASC_CAR * one + BETA_COST * car_cost + BETA_TIME * car_time 1 Rail one ASC_RAIL * one + BETA_COST * rail_cost + BETA_TIME * rail_time AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
14 BIOGEME - Model file [Expressions] // Define here arithmetic expressions for name that are not directly // available from the data one = 1 [Model] // Currently, only $MNL (multinomial logit), $NL (nested logit), $CNL // (cross-nested logit) and $NGEV (Network GEV model) are valid keywords // $MNL AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
15 Model and Data Files How to read and modify model files? How to read data files? GNU Emacs, vi, TextEdit (Mac) or Wordpad (Windows) Notepad (Windows) should not be used! AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
16 BIOGEME - Results - Netherlands dataset AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
17 BIOGEME - Results General model information AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
18 BIOGEME - Results Coefficient estimates AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
19 Today Further introduction to BIOGEME Estimation of Binary Logit models AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
20 Binary Logit Case Study Dataset: mode choice in Netherlands Description available on the course webpage. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
21 How to go through the Case Studies Download the files related to the case study from the course webpage. Go through the.mod files with the help of the descriptions. Run the.mod files with BIOGEME. Interpret the results and compare your interpretation with the one we have proposed. Develop other model specifications. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
22 Course webpage Teaching Decision-aid methodologies in transportation Laboratories BIOGEME software (including documentation and utilities) For each Case Study: Data files; Model specification files; Possible interpretation of results. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
23 Today s plan Group work gather in groups; generate.mod file (base); test an idea/ hypothesis. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
24 Specifying models: Recommended steps Formulate a-priori hypothesis: Expectations and intuition regarding the explanatory variables that appear to be significant for mode choice. Specify a minimal model: Start simple; Include the main factors affecting the mode choice of (rational) travelers; This will be your starting point. Continue adding and testing variables that improve the initial model.. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
25 Evaluating models The main indicators used to evaluate and compare the various models are summarised here: Informal tests: signs and relative magnitudes of the parameters β values (under our a-priori expectations); trade-offs among some attributes and ratios of pairs of parameters (e.g. reasonable value of time). Overall goodness of fit measure: adjusted rho-square (likelihood ratio index): takes into account the different number of explanatory variables used in the models and normalizes for their effect suitable to compare models with different number of independent variables. We check this value to have a first idea about which model might be better (among models of the same type), but it is not a statistical test. AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
26 Evaluating models (cont.) Statistical tests: t-test values: statistically significant explanatory variables are denoted by t-statistic values remarkably higher/ lower than ±2 (for a 95% level of confidence); final log-likelihood for the full set of parameters: should be remarkably different from the ones in the naive approach (null log-likelihood and log-likelihood at constants); we ask for high values of likelihood ratio test [ 2(LL(0) LL(β))] in order to have a model significantly different than the naive one. Test of entire models: likelihood ratio test [ 2(LL(ˆβ R ) LL(ˆβ U ))]: used to test the null hypothesis that two models are equivalent, under the requirement that the one is the restricted version of the other. The likelihood ratio test is X 2 distributed, with degrees of freedom equal to K U K R (where K the number of parameters of the unrestricted and restricted model, respectively). AFA (TRANSP-OR) Computer Lab 9 April 26, / 26
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