1. Introduction to Multilevel Modeling Using SPSS
David A. Kenny

2. Outline
Introduction
Extended Illustrations
Other Topics

3. 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.

4. 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

5. 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

6. 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

7. 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.

8. 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.

9. 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.

10. 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.

11. 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

12. 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)

13. 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.

14. 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)

15. 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.

16. 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

17. References
Go to references.
Go to “Other Topics”