Hello Charlie. This looks like an interesting research question. However, I do have a few comments on the interpretation and statistical modelling. Both statistical comments are on subtle issues, which I would not expect an undergraduate to be aware of. Many PhD students won’t be aware of them either!
On interpretation with respect to the Easterlin paradox: your working model, as far as I can tell, appears to assume that quit rates decrease in a person’s latent happiness, but not in their reported happiness. However, if shifts in reporting are caused by social comparisons (i.e., all the other jobs or relationships you see around you improving) then from that direction rescaling no longer implies a flatter relationship, as the quality of the jobs or relationships available upon quitting have increased. However, your results are indicative that other forms of rescaling are not occurring e.g., changes in culture. I think this distinction is important for interpretation.
The first of the statistical comments that these changes in probabilities of making a change could also be explained by a general increase in the ease of or tendency to get a hospital appointment/new job. This stems from the non-linearity of the logistic function. Logistic regression models a latent variable that determines the someone’s tendency to quit and converts this into a probability. At low probabilities, an increase in this latent variable has little effect on the probability of separation due to the flatness of the curve mapping the latent variable into probabilities. However, the same increase at values of the variable that give probabilities closer to 0.5 will have a big effect on the probability of separation as the curve is steep in this region. As your research question is conceptual (you’re interested in whether life satisfaction scales map to an individual’s underlying willingness to quit in the same way over time), rather than predicting the probability of separations, the regression coefficients on time interacted with life satisfaction should be the parameter of interest rather than the probabilities. These effects can often go in different directions. A better explanation of this issue with examples is available here: https://datacolada.org/57 I also don’t know whether results will be sensitive to assuming a logit functional form relative to other reasonable distributions, such as a probit.
Another more minor comment, is that you need to be careful when adding individual fixed effects to models like this, which you mentioned you did as a robustness check. In non-linear models, such as a logit, doing this often creates an incidental parameters problem that make your regression inconsistent. In this case, you would also be dealing with the issue that it is impossible to separately identify age, time, and cohort effects. Holding the individual constant, the coefficient of a change in time with life satisfaction would include both the time effect you are interested in and an effect of ageing that you are not.
I’d be happy to discuss any of these issues with you in more detail.
Hello Charlie. This looks like an interesting research question. However, I do have a few comments on the interpretation and statistical modelling. Both statistical comments are on subtle issues, which I would not expect an undergraduate to be aware of. Many PhD students won’t be aware of them either!
On interpretation with respect to the Easterlin paradox: your working model, as far as I can tell, appears to assume that quit rates decrease in a person’s latent happiness, but not in their reported happiness. However, if shifts in reporting are caused by social comparisons (i.e., all the other jobs or relationships you see around you improving) then from that direction rescaling no longer implies a flatter relationship, as the quality of the jobs or relationships available upon quitting have increased. However, your results are indicative that other forms of rescaling are not occurring e.g., changes in culture. I think this distinction is important for interpretation.
The first of the statistical comments that these changes in probabilities of making a change could also be explained by a general increase in the ease of or tendency to get a hospital appointment/new job. This stems from the non-linearity of the logistic function. Logistic regression models a latent variable that determines the someone’s tendency to quit and converts this into a probability. At low probabilities, an increase in this latent variable has little effect on the probability of separation due to the flatness of the curve mapping the latent variable into probabilities. However, the same increase at values of the variable that give probabilities closer to 0.5 will have a big effect on the probability of separation as the curve is steep in this region. As your research question is conceptual (you’re interested in whether life satisfaction scales map to an individual’s underlying willingness to quit in the same way over time), rather than predicting the probability of separations, the regression coefficients on time interacted with life satisfaction should be the parameter of interest rather than the probabilities. These effects can often go in different directions. A better explanation of this issue with examples is available here: https://datacolada.org/57 I also don’t know whether results will be sensitive to assuming a logit functional form relative to other reasonable distributions, such as a probit.
Another more minor comment, is that you need to be careful when adding individual fixed effects to models like this, which you mentioned you did as a robustness check. In non-linear models, such as a logit, doing this often creates an incidental parameters problem that make your regression inconsistent. In this case, you would also be dealing with the issue that it is impossible to separately identify age, time, and cohort effects. Holding the individual constant, the coefficient of a change in time with life satisfaction would include both the time effect you are interested in and an effect of ageing that you are not.
I’d be happy to discuss any of these issues with you in more detail.