Prediction probabilities from MDCEV model

[Pigouvian]

Hi Stephane and David!

I would like to confirm whether the following output variables from the MDCEV model refer to:

cont_sd: Standard deviation of predicted continuous consumption (i.e., time allocated to an activity),
disc_sd: Standard deviation of the discrete 0/1 choice decision (whether an activity is chosen or not), and
expe_sd: Standard deviation of expected utility across alternatives or choice occasions.

Additionally, I seek clarification on the interpretation of these standard deviation measures. Specifically:
Do these standard deviations primarily represent modeling uncertainty (i.e., the error or unexplained variation arising because the model cannot fully capture all aspects of decision-making behavior)? Or, in the case of panel data, do they instead reflect intra-individual variability in behavior—that is, the genuine variation in an individual’s activity choices or time use across different days?

If the latter interpretation is valid (i.e., these standard deviations capture actual behavioral variability across repeated observations), can they then be used in further statistical analysis, for example, as dependent variables in models of instability in activity engagement patterns?

[dpalma]

Hi,

You are correct about cont_sd and disc_sd, but not expe_sd.

Before defining them it is important to understand how the forecast of MDCEV is calculated. The forecast is based on simulation. For each row in your data, a draw for each good or alternative is drawn, then the consumer utility maximisation problem is solved. The process is repeated multiple times for each individual (by default 100 times, but you can change it with the setting nRep), and the final forecast is the average across all those repetitions.

Then the reported measures as defined as follows:

• cont_sd: The standard deviation of the continuous consumption for each row in the data, across all repetitions. Repetitions where this alternative was not consumed are included in the calculation.
• disc_sd: Standard deviation of a binary variable (0/1) indicating if an alternative was (1) or not (0) consumed during each repetition. The s.d. is calculated across all repetitions.
• expe_sd: Standard deviation of the expenditure (continuous_consumption*price) for eac row of your data, across all repetitions.

Concerning interpretation, these standard deviations measure the variability due to the model's error term (epsilon), which is usually considered to capture unobserved (for the modeller) variability, such as relevant factors that could not be captured in the database. But this variability is usually not associated to unstable preferences by the decision maker, in other words, preferences are assumed to remain stable from one choice to the next of the same individual. So I would say your first interpretation is the most accurate one.

Can these levels of variability be used in further statistical analysis? Depends on what you want to do. If you wanted to simulate decisions, you could use them to define probability distributions for each outcome (e.g. activity engagement in a transport activity-based model). But if that was the case, it would be better to simulate the utilities (including drawing from their epsilons), and solve the optimisation problem, as that would ensure your forecast respected the budget.

Best wishes,
David