Interpreting Discrete Choice Models

Discrete choice models are nonlinear, so interpretive techniques such as first differences, marginal effects, and elasticities are used to understand the magnitude of effects on choice behavior. These techniques can be applied to other models with discrete dependent variables.

Format: Paperback / softback
Length: 75 pages
Publication date: 12 May 2022
Publisher: Cambridge University Press

In discrete choice models, the relationships between independent variables and choice probabilities exhibit nonlinear characteristics, influenced by both the value of a specific independent variable and the values of other independent variables. Consequently, interpreting the magnitude of the effects (referred to as "substantive effects") of these independent variables on choice behavior necessitates the application of additional interpretative techniques. Here, we will explore three commonly employed techniques for interpretation: first differences, marginal effects, and elasticities, along with odds ratios. Additionally, we will delve into concepts related to these techniques, as well as methods to account for estimation uncertainty.

First, let us consider first differences. First differences measure the change in the choice probability resulting from a change in the value of a single independent variable while holding all other variables constant. By calculating the first difference between the choice probability with and without the change in the independent variable, we can obtain an estimate of the substantive effect of that variable on choice behavior.

Next, we turn to marginal effects. Marginal effects provide insights into the change in the choice probability associated with a one-unit change in the value of a specific independent variable, while all other variables remain at their original values. These effects help us understand the direction and magnitude of the influence of each independent variable on choice behavior.

Elasticities, on the other hand, quantify the responsiveness of the choice probability to changes in the values of independent variables. They indicate the percentage change in the choice probability resulting from a one-percentage point change in the value of the respective variable. Elasticities provide valuable information about the strength and direction of the relationships between independent variables and choice probabilities.

Lastly, odds ratios are a measure of the relative odds of choosing one option over another. They compare the choice probability of a specific group (e.g., males) with the choice probability of another group (e.g., females) when all other variables are held constant. Odds ratios help us assess the relative influence of different independent variables on choice behavior, particularly when the dependent variable is categorical.

In addition to these interpretative techniques, it is important to consider concepts related to them. For instance, the concept of partial effects allows us to decompose the total effect of an independent variable into its direct and indirect effects on choice behavior. This decomposition helps us understand the specific contributions of each variable to the overall outcome.

Furthermore, methods to account for estimation uncertainty are crucial in interpreting discrete choice models. Techniques such as bootstrapping, jackknifing, and cross-validation can provide robust estimates and improve the reliability of our interpretations.

Now, let us turn our attention to the interpretation of binary logits, ordered logits, multinomial and conditional logits, and mixed discrete choice models for panel data. These models are commonly used in empirical studies of consumer behavior and other fields.

Binary logits model the choice between two options, typically represented as a binary variable (e.g., yes/no, male/female). The interpretation of binary logits involves estimating the parameters of the model and interpreting the effects of the independent variables on the choice probability. Marginal effects, elasticities, and odds ratios can be used to analyze the effects of different variables on the choice between the two options.

Ordered logits models allow for the ordinal nature of the dependent variable, where the choices are ranked or ordered. The interpretation of ordered logits involves estimating the parameters of the model and interpreting the effects of the independent variables on the rank or order of the choices. Marginal effects, elasticities, and odds ratios can also be used to analyze the effects of different variables on the rank or order of choices.

Multinomial and conditional logits models allow for the presence of multiple choices or categories. The interpretation of these models involves estimating the parameters of the model and interpreting the effects of the independent variables on the choice probabilities or the probabilities of choosing specific categories. Marginal effects, elasticities, and odds ratios can be used to analyze the effects of different variables on the choice probabilities or the probabilities of choosing specific categories.

Mixed discrete choice models, such as mixed multinomial logits and random effects logits for panel data, incorporate both continuous and categorical independent variables. The interpretation of these models involves estimating the parameters of the model and interpreting the effects of the continuous and categorical variables on the choice probabilities or the probabilities of choosing specific categories. Marginal effects, elasticities, and odds ratios can be used to analyze the effects of different variables on the choice probabilities or the probabilities of choosing specific categories.

In conclusion, the interpretation of discrete choice models requires the application of various interpretative techniques, including first differences, marginal effects, and elasticities, along with odds ratios. These techniques help us understand the magnitude and direction of the effects of independent variables on choice behavior. By considering concepts related to these techniques, such as partial effects and estimation uncertainty, we can enhance our understanding of the underlying relationships between variables and choice outcomes. The techniques discussed here are general and can be applied to other models with discrete dependent variables that are not specifically described here.

ISBN-13: 9781108819404