45. Random Intercept for Categorical Outcome and Predictor Variables (55 Patients)

Categories are very common in medical research. Examples include age classes, income classes, education levels, drug dosages, diagnosis groups, disease severities, etc. Statistics has generally difficulty to assess categories, and traditional models require either binary or continuous variables. If in the outcome, categories can be assessed with multinomial regression (Chap. 44). If as predictors, they can be assessed with linear regression for categorical predictors (Chap. 8). However, with multiple categories or with categories both in the outcome and as predictors, random intercept models may provide better sensitivity of testing. The latter models assume that for each predictor category or combination of categories x₁, x₂,…slightly different a-values can be computed with a better fit for the outcome category y than a single a-value. We should add that, instead of the above linear equation, even better results were obtained with log-transformed outcome variables (log = natural logarithm).

Are in a study of exposure and outcome categories the exposure categories significant predictors of the outcome categories. Does a random intercept provide better test-statistics than does a fixed effects analysis.

In a study, three hospital departments (no surgery, little surgery, lot of surgery), and three patient age classes (young, middle, old) were the predictors of the risk class of falling out of bed (fall out of bed no, yes but no injury, yes and injury). Are the predictor categories significant determinants of the risk of falling out of bed with or without injury. Does a random intercept provide better statistics.

Only the first 10 patients of the 55 patient file is shown above. The entire data file is in extras.springer.com and is entitled “chapter45randomintercept.sav”. SPSS version 20 and up can be used for analysis. First, we will perform a fixed intercept model.

The module Mixed Models consists of two statistical models:

For analysis the statistical model Generalized Linear Mixed Models is required.

First we will perform a fixed effects model analysis, then a random effects model.

The underneath results show that both the various regression coefficients as well as the overall correlation coefficients between the predictors and the outcome are, generally, statistically significant.

Subsequently, a random intercept analysis is performed.

The underneath results show the test-statistics of the random intercept model. The random intercept model shows better statistics:

In the random intercept model we have also commanded predicted values (variable 7) and predicted probabilities of having the predicted values as computed by the software (variables 5 and 6).

Like automatic linear regression (see Chap. 7), and other generalized mixed linear models (see Chap. 12), random intercept models include the possibility to make XML files from the analysis, that can subsequently be used for making predictions about the chance of falling out of bed in future patients. However, SPSS uses here slightly different software called winRAR ZIP files that are “shareware”. This means that you pay a small fee and be registered if you wish to use it. Note that winRAR ZIP files have an archive file format consistent of compressed data used by Microsoft since 2006 for the purpose of filing XML (eXtended Markup Language) files. They are only employable for a limited period of time like e.g. 40 days.

Generalized linear mixed models are suitable for analyzing data with multiple categorical variables. Random intercept versions of these models provide better sensitivity of testing than fixed intercept models.

More information on statistical methods for analyzing data with categories is, e.g., in the Chaps. 8, 39, and 44.