I have a dependent variable made up of 3 categories and 14 binary predictor variables.
I have tried using mlogit and nnet/multinom packages in R.
Is there a better approach than multinomial logistic regression for this particular scenario?
Solved – Whether to use multinomial logistic regression with a three-category outcome variable and many binary predictors
logisticmultinomial-distributionr
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In a multinomial logistic regression with 3 levels of the DV there ought to be two intercepts. How exactly these are defined depends on which is the reference level. These will be the value of the logit when the independent variables are 0, in your case, when risk is high.
I wrote a presentation on multinomial and ordinal logistic regression; it somewhat concentrated on SAS, but some may be useful even if you are using another package.
If $Y$ has more than two categories your question about "advantage" of one regression over the other is probably meaningless if you aim to compare the models' parameters, because the models will be fundamentally different:
$\bf log \frac{P(i)}{P(not~i)}=logit_i=linear~combination$ for each $i$ binary logistic regression, and
$\bf log \frac{P(i)}{P(r)}=logit_i=linear~combination$ for each $i$ category in multiple logistic regression, $r$ being the chosen reference category ($i \ne r$).
However, if your aim is only to predict probability of each category $i$ either approach is justified, albeit they may give different probability estimates. The formula to estimate a probability is generic:
$\bf P'(i)= \frac{exp(logit_i)}{exp(logit_i)+exp(logit_j)+\dots+exp(logit_r)}$, where $i,j,\dots,r$ are all the categories, and if $r$ was chosen to be the reference one its $\bf exp(logit)=1$. So, for binary logistic that same formula becomes $\bf P'(i)= \frac{exp(logit_i)}{exp(logit_i)+1}$. Multinomial logistic relies on the (not always realistic) assumption of independence of irrelevant alternatives whereas a series of binary logistic predictions does not.
A separate theme is what are technical differences between multinomial and binary logistic regressions in case when $Y$ is dichotomous. Will there be any difference in results? Most of the time in the absence of covariates the results will be the same, still, there are differences in the algorithms and in output options. Let me just quote SPSS Help about that issue in SPSS:
Binary logistic regression models can be fitted using either the Logistic Regression procedure or the Multinomial Logistic Regression procedure. Each procedure has options not available in the other. An important theoretical distinction is that the Logistic Regression procedure produces all predictions, residuals, influence statistics, and goodness-of-fit tests using data at the individual case level, regardless of how the data are entered and whether or not the number of covariate patterns is smaller than the total number of cases, while the Multinomial Logistic Regression procedure internally aggregates cases to form subpopulations with identical covariate patterns for the predictors, producing predictions, residuals, and goodness-of-fit tests based on these subpopulations. If all predictors are categorical or any continuous predictors take on only a limited number of values—so that there are several cases at each distinct covariate pattern—the subpopulation approach can produce valid goodness-of-fit tests and informative residuals, while the individual case level approach cannot.
Logistic Regression provides the following unique features:
- Hosmer-Lemeshow test of goodness of fit for the model
- Stepwise analyses
- Contrasts to define model parameterization
- Alternative cut points for classification
- Classification plots
- Model fitted on one set of cases to a held-out set of cases
- Saves predictions, residuals, and influence statistics
Multinomial Logistic Regression provides the following unique features:
- Pearson and deviance chi-square tests for goodness of fit of the model
- Specification of subpopulations for grouping of data for goodness-of-fit tests
- Listing of counts, predicted counts, and residuals by subpopulations
- Correction of variance estimates for over-dispersion
- Covariance matrix of the parameter estimates
- Tests of linear combinations of parameters
- Explicit specification of nested models
- Fit 1-1 matched conditional logistic regression models using differenced variables
Best Answer
Given your description of the situation, you are using the right model. There is no problem with having discrete IVs with multinomial logistic regression; MLR does not make any assumptions about the nature or distribution of the IVs. However, I wonder if your IVs are not orthogonal. It's hard to tell, but you may be describing some effects of multicollinearity.
I'm not sure what happened with R, you would need to show your code and data and perhaps the error messages for someone to help you figure that out. Questions about those sorts of issues should be asked on Stack Overflow or the R-help mailing list, though; they are off topic here.