I want to ask you a question about data analysis in psychology. I have two independent variables, one is group (between subjects), one is age (continuous data), and the dependent variable is a 6-point Likert score. I intend to use regression for data analysis, with three questions:
1. Should the ID of the subjects (the number of each subject) be included in the model as a random variable? If it is included, it should be Linear Mixed Model (LMM), if it is not included, it should be Multiple Linear Regression, right?
2. In the case of multiple linear regression, should I directly build the full model and see the influence of each independent variable, or should I build the full model and compare with the zero model, and then analyze with the method of step by step elimination?
3. When I do my analysis, do I need to centralize both age (continuous variable) and rating, or do I just need to centralize age?
1.Subject ID inclusion as a random variable is appropriate if you have repeated measures or a nested structure in your data. If each subject contributes only one data point, it's Multiple Linear Regression. If subjects contribute multiple data points, consider Linear Mixed Model (LMM) to account for potential correlations within subjects. LMM is most recommended for repeated measures dispositions.
2.The good practice is to start with the full model, then assess variable importance. You can compare with a null model, but stepwise methods (like stepwise elimination) can introduce issues (like Type I errors). Consider using model selection techniques like backward elimination based on a priori knowledge or criteria such as AIC.
3.To reduce multicollinearity, centering age is generally recommended and this aid in interpretation. Centering the Likert scores may be optional and depends on your research question. Centering helps interpret the intercept as the expected value when all predictors are at their means. Consider your hypotheses and the interpretation you want for meaningful centering choices.
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