Introduction to Multilevel Modeling Using SPSS David A. Kenny

Outline Introduction Extended Illustrations Other Topics

Why SPSS? Relatively simple and accessible Not always the best program available Some analyses are currently impossible with SPSS. Sometimes SPSS has no solution whereas other programs do. Better tests of variance components in other programs. Will see examples of other programs on the Nested webinar.

Names and Structure Alternative names Hierarchical linear modeling (HLM) not to be confused with the computer program HLM Random coefficient regressions Mixed model ANOVA Data structure a hierarchical or nested structure (tree-like structure) sets of units are members of some higher-order set e.g., each person in one group less common: a crossed structure factorial design e.g., each person in more than one group

Two Major Uses of Multilevel Modeling Persons within groups Groups or dyads Organizations or schools Interaction partners Observations within persons Standard repeated measures design Diary studies Web surveys Longitudinal research

Advantages over Conventional Analyses Proper standard errors and p values Missing data not problematic Unequal spacing of observations in over-time analyses not problematic Continuous covariates not required More information

Two Levels (can be more than two) lower level: level 1 -- observation or person upper level: level 2 -- person or group  Types of Variables level 1: a measurement for each observation the outcome as a level-1 variable level 2: a single measurement for each upper-level unit cross-level effects: the interaction of a level 1 with a level 2 variable The designation of variables as level 1 and level 2 is not required for some computer programs (it is for HLM, but not for SPSS), but it helps to know the level for the variable.  

Multilevel Modeling as a Two-Step Procedure Step 1: For each level 2 unit, regression the outcome on level 1 predictors. Step 2: Using the coefficients from the level 1 analysis as the outcome, see what level 2 predictors can explain their variation. In actuality, not done this way, but it helps to think initially about things this way.

Fixed and Random Effects In ANOVA or multiple regression, the fixed effects are the means or regression coefficients. The random effect is the error variance. For MLM, as there are two levels, there can multiple sources of variance. As will be seen, there can also be a correlation of random effects at the same level.

Centering Definition: removing the mean from the raw data before undertaking statistical analyses Method: Besides subtracting the mean, subtract the median or a “typical value.” Goal: To make zero a meaningful value; if zero is not a plausible score, some sort of centering is necessary.  

What Variables to Center and Why? the outcome variable: not advisable The intercept is the predicted score when all predictors equal zero. predictor variables: generally must center in some way level 1 variables level-1 intercepts are usually interpreted level-2 variables the intercepts of level-2 equations need to be meaningful as they represent the predicted slope, given zero on the level-2 variables variances differ depending on how the centering is done zero needs to be meaningful for the level-2 variables

Estimation Maximum Likelihood (ML) or Restricted Maximum Likelihood (REML, the preferred and typically the default method, because variances unbiased with small samples) All parameters estimated simultaneously Estimates assume a normal distribution of all random effects Solution iterative (usually no closed formed formula for estimates)

Iteration and Convergence Must have valid estimates of variances before examining the fixed effects. Solution iterative (usually no closed formed formula for estimates) Sometimes model does not converge: especially when the model contains “too many” random effects or random effects that are small.

Parameter Testing test of variance Wald test (what SPSS gives) likelihood ratio test not advisable to trim out non-significant covariances fixed effects t tests (with fractional df)

Model Fit The fit of the model is given by the model’s “deviance,” called “-2LogLikelhood” in SPSS. Deviances of different nested models can be compared using a c2 test. Can use REML as the estimation method if fixed effects are the same If fixed effects are different, must use ML.

Illustrations Two-level Nesting Kashy diary study Growth-curve Campbell et al. study of satisfaction over time Repeated Measures Cook study of mothers and family members. Two-intercept Campbell et al. study of doctors and patients Crossed Design Smith-McLallen et al. IAT study

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