Can I use a dichotomous dependent variable in a mixed model (e.g., logistic mixed model)?

[#1]

If I choose the mixed model personality then select a dichotomous dependent variable it jumps out of the mixed model personality. I can run "nominal Logistic" regression, but that no longer gives me the estimates for the random effects.

[#2]

No, the mixed model personality in JMP Pro supports only normally distributed dependent variables.  

[#3]

Great, thanks for the reply.

Jeff

[#4]

Hi again,

Well, now that I’ve solved my other problem I want to come back to this one (logistic Mixed Model).

Because I was unable to run the logistic mixed model I thought I should use, I ran two other analyses.

In one analysis I used Nominal Logistic Personality using the Fit Model Dialogue, and in the other I switched the dichotomous dependent variable to a continuous variable.

The fixed effects are very similar across analyses, and lead to the same conclusions, although the mixed model gives the added information of the random effects of the within-subjects factor.

So, my question is whether one solution is clearly off limits (e.g., forcing the dichotomous variable to be treated a continuous), or whether the added advantage of having information on the random effects outweighs the risks introduced by forcing the DV to be continuous. All of this is in the context in which the fixed effects don’t change much (conclusions don’t change) across the two analyses.

Thanks again, Jeff

[#5]

Treating a dichotomous response variable as a continuous one on a 0-1 scale leads to a so-called "linear probability model" in literature. A key criticism concerns the fitted probabilities lying outside the probability limits (0,1) . 

Without seeing your analyses I could only offer my general comments on your findings "The fixed effects are very similar across analyses, and lead to the same conclusions": (1) The coefficients from a logistic regression represent the log odd ratios, while the coefficients from a linear regression model are the marginal effects. They usually are not the same or even close in magnitude; (2) Random-effect models often yields more efficient estimates, so the conclusion about the statistical significance of a fixed effect can be different.    

[#6]

Hi again,

and thank you again for all of your help.

I’ve attached the data file that I’m working with.

There is only one script saved, which was created using the Repeated Measure add in, but is the same analysis that comes out using the mixed model dialogue with the DV treated as continuous.

So, if you run the saved script with the data as they are you get a random effects model, and although the variable itself is defined as nominal, there results are identical to those in which the DV is defined as continuous (does that simply mean that JMP is making a mistake and running the analysis treating the dichotomous DV as continuous?).

If you then switch the personality to nominal logistic the results change, but as you can see the pattern of results (e.g. p values and conclusions) remains the same.

Recommendations?

Thank you again.

Best, Jeff

[#7]

The add-in you referred to supports continuous response variables only--"This Add-In generates the linear mixed-effects (random- and fixed-effect) model terms for one-way or full factorial repeated-measures designs involving a continuous response variable (categorical responses are not supported at this time)" https://community.jmp.com/docs/DOC-6993

So the Add-in does the analysis by treating your numerical nominal variable as continuous on a [0, 1] scale, That is why you find the results identical to the results from the Mixed Model personality.

RE: "If you then switch the personality to nominal logistic the results change, but as you can see the pattern of results (e.g. p values and conclusions) remains the same."

I do see in this data the same significance pattern of p-values in the Fixed effect Test report from Mixed Models and in the Effect LR Tests report, but it is not always the case. Also, see my comments about the difference between the LPM and logistic regression in my previous reply. 

[#8]

Thank you again for your very clear and fast assistance. Best, Jeff

[#9]

Now there is this: