I will mainly focus on your first three questions. The short answers are: (1) you need to compare the effect of the IV on the DV for each time period but (2) only comparing the magnitudes can lead to wrong conclusions, and (3) there are many ways of doing that but no consensus on which one is correct.
Below I describe why you cannot simply compare coefficient magnitudes and point you to some solutions that have been thought of so far.
According to Allison (1999), unlike OLS, logistic regression coefficients are affected by unobserved heterogeneity even when such heterogeneity is not related to the variable of interest.
When you fit a logistic regression like:
(1)$$
\ln\bigg(\frac{1}{1-p_i}\bigg) = \beta_{0} + \beta_{1}x_{1i}
$$
You are in fact fitting an equation predicting the value of a latent variable $y^*$ that represents the underlying propensity of each observation to assume the value $1$ in the binary dependent variable, what happens if $y^*$ is above a certain threshold. The equation for that is (Williams, 2009):
(2)$$
y^* =\alpha_{0} + \alpha_{1}x_{1i} + \sigma \varepsilon
$$
The term $\varepsilon$ is assumed to be independent from the other terms and to follow a logistic distribution – or a normal distribution in the case of probit and a log-logistic distribution in case of complementary log-log and a cauchy distribution in the case of cauchit.
According to Williams (2009), the $\alpha$ coefficients in equation 2 are related to the $\beta$ coefficients in equation 1 through:
(3)$$
\beta_{j} = \frac{\alpha_{j}}{\sigma}\;\;j=1,...,J.
$$
In equations 2 and 3, $\sigma$ is the scaling factor of the unobserved variation, and we can see that the size of the estimated $\beta$ coefficients depends on $\sigma$, which is not observed. Based on that, Allison (1999), Williams (2009), and Mood (2009), among others, claim that you cannot naively compare coefficients between logistic models estimated for different groups, countries or periods.
This is because comparisons may yield incorrect conclusions if the unobserved variation differs between groups, countries or periods. Both comparisons using different models and using interaction terms within the same model suffer from this problem. Besides logit, this also applies to its cousins probit, clog-log, cauchit and, by extension, to discrete time hazard models estimated using these link functions. Ordered logit models are also affected by it.
Williams (2009) argues that the solution is to model the unobserved variation through a heterogeneous choice model (a.k.a., a location-scale model), and provides a Stata add on called oglm for that (Williams 2010). In R, heterogeneous choice models can be fit with the hetglm() function of the glmx package, which is available through CRAN. Both programs are very easy to use. Lastly, Williams (2009) mentions SPSS's PLUM routine for fitting these models, but I have never used it and cannot comment in how easy it is to use.
However, there is at least one working paper out there showing that comparisons using heterogeneous choice models can be even more biased if the variance equation is misspecified or there is measurement error.
Mood (2010) lists other solutions that do not involve modelling the variance, but use comparisons of predicted probability changes.
Apparently it is an issue that is not settled and I often see papers in conferences of my field (Sociology) coming up with different solutions for it. I would advise you to look at what people in your field do and then decide how to deal with it.
References
- Allison, P. D. (1999). Comparing Logit and Probit Coefficients Across Groups. Sociological Methods & Research, 28(2), 186–208.
- Mood, C. (2010). Logistic Regression: Why We Cannot Do What We Think We Can Do, and What We Can Do About It. European Sociological Review, 26(1), 67–82.
- Williams, R. (2009). Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients Across Groups. Sociological Methods & Research, 37(4), 531–559.
- Williams, R. (2010). Fitting heterogeneous choice models with oglm. The Stata Journal, 10(4), 540–567.
Best Answer
Sounds like you need an interaction term between
walk_timeandtrain_time. Certainly not three separate models.If I've understood your setup right and if people tend to want to minimise or lower bound total travel time, then I would expect these two variables to be negatively related as people trade them off.
In SPSS I believe you have to construct interaction terms manually. The web is full of people who'll show you how to do that. Then you have to interpret the interaction properly. That will require a little reading, but any regression textbook should cover it.