I am totally new to LCA but have conducted a latent class analysis in R using the glca package and found a 4 class model to be preffered according to fit values (BIC, AIC, Entropy). I am now trying to add in gender as a covariate but not quite sure how to interpret the results. I understand that the output is comparing class 1 to 4, 2 to 4etc for class differences. I have Gender_Binary as my gender variable with values male=1, female=2 but which value (e.g male or female) is being displayed in the output? Can anyone provide a basic analysis of what this output shows or suggest some good LCA guides for R?
Class 1 / 4 :
Odds Ratio Coefficient Std. Error t value Pr(>|t|)
(Intercept) 16.34772 2.79409 0.64192 4.353 1.77e-05 ***
Gender_Binary 0.04619 -3.07509 0.52766 -5.828 1.27e-08 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Class 2 / 4 :
Odds Ratio Coefficient Std. Error t value Pr(>|t|)
(Intercept) 4.9731 1.6040 0.4526 3.544 0.000447 ***
Gender_Binary 0.2294 -1.4725 0.2922 -5.039 7.5e-07 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Class 3 / 4 :
Odds Ratio Coefficient Std. Error t value Pr(>|t|)
(Intercept) 0.1466 -1.9199 0.8710 -2.204 0.0282 *
Gender_Binary 1.1356 0.1272 0.4794 0.265 0.7909
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
The "Coefficient" column gives you the logistic regression intercept and slope coefficients. Currently, the intercepts do not have a meaningful interpretation in your model because of your coding of the gender groups as 1 (male) and 2 (female). Consequently, there is no group with the value of zero (0) and therefore, the intercepts don't have any meaningful interpretation.
First of all, I would recommend recoding the gender groups as 0 (male) and 1 (female) so that your logistic regression intercept coefficients have a meaningful interpretation as the log odds in the group that is coded 0 (male). This recoding will not affect the logistic regression slope coefficients--they will stay the same.
The slope coefficients (under "Gender_Binary") give the difference in log odds between the two gender groups. If the slope coefficient is negative, this means that the log odds is smaller in group female as compared to group male.
Once you recode gender as 0 (male) and 1 (female), the sum of intercept and slope coefficients for a given class comparison will give you the log odds in group female.
Attached are some powerpoint slides from my LCA online course (https://www.goquantfish.com/courses/latent-class-analysis-with-mplus) in which I explain the meaning of logistic regression coefficients and odds ratios in LCA with binary covariates (note that the coding in my example is 0 = female, 1 = male, so it's different from yours). My example uses Mplus but the interpretation of the logistic regression results is the same. Hopefully, the slides can help you figure out the correct interpretation of the coefficients in your case.
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