Complement Probit coefficients with OR and predicted probabilities

[fernando vazquez]

Dear friends of Statalist, good morning.

I am a doctor from Argentina (MD, PhD, MSC), and I work at the Hospital Italiano in Buenos Aires.

I am investigating MIMIC (Multiple IndicatorsMultiple Causes) models since with them I can do regressions, including factors (made up of several items), and the observed variables (glycemia, cholesterol, blood pressure, etc.). All together.

I work with RStudio, and I have the Probit coefficients as a result. Since the interpretation of Probit coefficients is not very "intuitive", think about helping the reader with these two methodologies:

1) I am considering, in addition to the Probit regression result, offering the reader an estimate of the odds ratio, first multiplying by 1.7 to obtain the logit coefficients (Scott Long, 2014), and then applying the exponential function (the natural anti-logarithm ), to the estimated value of the logit coefficient, to calculate the odds ratio.

2) Additionally, with STATA, calculate the predicted probabilities of the independent variable that interests me the most, with the command:

“margins , at (variable =(())) vsquish”.

Where I can place, as adjustment variables, the other observed variables, and also the variables or items that make up the factors (since I cannot directly include the factors, or latent variables).

Does it seem appropriate to you, to complement the results?

[Clyde Schechter]

The 1.7 factor to get logit from probit coefficients is just an approximation. And when you then exponentiate the result, you are likely to inflate the approximation error still farther. I'm not a big fan of this approach. If your concern is that probit coefficients are difficult to interpret (and I agree that they are) and you think logit estimates are more comprehensible, why not just use logit models in the first place?

As for your question about the -margins- command, there is no need to mention any of the other variables when you use -margins-. The -margins- command automatically uses all of the model variables to adjust its results.

[fernando vazquez]

Thank you very much Clyde for your response. What happens is that MIMIC Models use Probit regressions. To my knowledge there are no MIMIC models with results in Logit coefficients

[Clyde Schechter]

To my knowledge there are no MIMIC models with results in Logit coefficients

I'll take your word for that. I think I have only done one MIMIC model in my entire career, and the indicators were continuous there anyway. Are you aware of any principled reason why a logit link couldn't be used in a MIMIC model? If there is a reason, then I suppose providing an approximation to the odds ratio is better than nothing. But if it is just a matter of custom to use probit in MIMIC models, I might, in your situation, present the models both ways: one with probit to permit direct comparison to the prevailing literature, and once with logit to give odds ratios for improved comprehensibility. I just don't like using approximation formulas when the exact calculations are easily implemented, and especially when a subsequent exponentiation is going to inflate the approximation error.

[fernando vazquez]

Thank you Clyde