Incorporating Response Latency as a Proxy for Measurement Error

Hi everyone,

I have a question that I hope you will find interesting.

Imagine I have a toy dataset of four variables:

  1. Respondent’s age (Continuous)
  2. Respondent’s gender (M/F)
  3. Whether the respondent would vote for incumbent party (Yes/No)
  4. Whether the respondent likes the leader of the incumbent party (Yes/No)

However, I also have paradata on how long it took each respondent to answer each question. This type of data is often used as an indicator of uncertainty (the longer it takes to answer, the more uncertain you are).

A simple voting model might look something like this:

Vote ~ 1 + Age + Gender + Leader

But it seems to me that this model (and by extension many, many others) assumes that all respondents are equally certain about their responses. That is, a ‘Yes’ response to question 3 that took 1 second, for example, is fundamentally different to one that took 20 seconds. Where respondents are less certain, then, it seems reasonable to expect that the relationship between the predictor and the outcome would be weaker.

I’d like to know how I can incorporate this uncertainty into the toy model above. I know that this is possible where we have standard errors for each of our predictors, but I’m less certain how to do this with response latency measures. In particular, I’d expect that response latency would not only be a function of uncertainty, but also of the respondent’s age, mode for answering the survey, etc.

Any ideas or advice would be much appreciated.

Thanks in advance,


Edit: grammar.

Maybe try having the latency (which you might want to log-transform) affect the noise term in that regression.

There isn’t a noise term in logistic regressions. And in linear regressions, the posterior parameter mean is independent of the noise scale, so it won’t help with regression coefficients.

You could assume there’s measurement error on the responses, the scale of which is dependent on latency. There’s a chapter in the manual on measurement error and you’d be adding in a predictor to determine the noise scale of the measurement error.

But given that it’s binary measurements, I’m not entirely sure how to do that.