Analyzing the effect of satisfaction on transport mode preference using mixed logistic regression in R

Question

I want to analyze the effect of satisfaction with different modes of transport (bus vs. train) on a specific route on stated preference. participants drove a specific route repeatedly with either bus or train as mainmode and filled out a satisfaction questionnaire. Each participant's total rides ranged from 5 to 10, leading to an unbalanced design.

DV: Preference (Bus =0, Train =1)

IVs for each ride: Mainmode (Bus = 1, Train = 2)
    Satisfaction Score (normally distributed)(TEc)

To answer my question I tried a mixed logistic regression in R. If a difference in satisfaction with bus or train rides has an influence on the preference, I would expect a significant fixed effect of their interaction (is this even correct?):

model <- glmer(bus_vs_train ~ TEc * Mainmode + (1 | Participant), 
               data = filtered_df, 
               family = binomial)

Output:
Nobs:354
nGroups:40


     AIC      BIC   logLik deviance df.resid 
    49.5     68.8    -19.7     39.5      349 

Fixed Effects	Estimate	Std. Error	z value	Pr(>z)
(Intercept)	14.1501	4.4655	3.169	0.00153
TEc	-0.5621	4.7430	-0.119	0.90566
Mainmode	0.2581	2.6815	0.096	0.92331
TEc:Mainmode	0.1237	2.8474	0.043	0.96534

Random Effects	Variance	Std.Dev.	Std.Dev.
Participant (Intercept)	5322	72.95

Model Summary
AIC	49.5
BIC	68.8
LogLik	-19.7
Deviance	39.5
Number of obs	354
Groups	40

No fixed effect is significant, and model fit is poor. Does this mean satisfaction with bus or train has no influence on preference? Is my analysis and interpretation correct?

Answer 1

You are dealing with a type of analysis that falls under the category of discrete choice modeling. This has a set of related but not equivalent approaches to modeling binary data such as yours.

There are books devoted to this topic, journal articles, and a host of web resources, including some Q&A on Cross Validated. I added the choice-modeling tag to your question so that folks who do this kind of modeling can perhaps chime in with feedback.

The bottom line is that you need to spend some time getting to know this modeling framework so that you can apply it to your data.