Interpreting odds ratio in logit models

[Meng Yu]

For my xtlogit model (though Stata shows "Random-effects logistic regression" in the table it produces), I used estout command to produce the results table. I am not quite certain how to interpret the odds ratios. If frequent participation in religious activities has an odds ratio of 0.71 and the reference group is presented as 1 with variance being 0, can I say "frequent participation reduces the odds of having mental health problems (dependent variable) by 0.29?"

Thank you.

[Meng Yu]

Or should I say "frequent participation reduces the odds of having mental health problems by 29% compared to no participation (ref group)?"

[Clyde Schechter]

Or should I say "frequent participation reduces the odds of having mental health problems by 29% compared to no participation (ref group)?"

That is the more correct way. But unless this is based on experimental data, it is not a good idea to use the term "reduces," which has connotations of causality. So better to say that "frequent participation is associated with a 29% lower odds of having mental health problems than non-participation."

[Meng Yu]

Thank you very much. I really appreciate it.

[Meng Yu]

I wonder if the word "predict" implies causality when we use longitudinal data and the independent variable "predicts" certain outcome in the dependent variable in the subsequent wave.

[Clyde Schechter]

No, the word predict does not imply causality. In fact, its meaning is explicitly neutral as to whether the variables doing the prediction are causally related to the outcome being predicted or not.

[Meng Yu]

Thank you.

[Meng Yu]

When we talk about associations using cross-sectional data, can we still use the word "predict"? Thanks.

[Clyde Schechter]

Yes.

[Meng Yu]

Thank you.

[Meng Yu]

I wonder when we use the expression "A has an effect on B," do we imply causality? Thank you.

[Clyde Schechter]

When speaking casually, one might talk about "the effect of A on B" to refer only to an estimate of marginal effect with no assumption about casuality. But in writing, or in formal oral presentations, it would be best to reserve the word "effect" for situations where we intend causality. At least that's my take on it.

[Meng Yu]

Thank you.

[Meng Yu]

I wonder when we use longitudinal data and fixed effects models, whether we can claim our findings to be causal. Thank you.

[Clyde Schechter]

I see the use of longitudinal data and fixed effects models as being neither here nor there with regard to causality.

Really the only firm basis for asserting causality is when analyzing data from a randomized controlled experiment. The next best thing is an experiment of nature. Then there are some still less reliable approaches to trying to identify causal effects from observational data such as difference-in-differences or instrumental variables. But all of these, other than the randomized controlled experiment, rely on some assumptions that often are only partly or weakly verifiable. All of these situations may involve longitudinal data and fixed effects models (especially difference-in-differences estimation), or they may use other kinds of data designs. And longitudinal data and fixed effects models can be used with plenty of data designs for which no claim of causality can be made.