Introduction - of David A. Kenny

Introduction to Multilevel
Modeling Using SPSS
David A. Kenny
January 7, 2014
•Extended Illustrations
•Other Topics
• Relatively simple and accessible
• Not always the best program available
– Some analyses are currently impossible with
– Sometimes SPSS has no solution whereas other
programs do.
– Better tests of variance components in other
• 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
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
• In ANOVA or multiple regression, the fixed
effects are the means or regression
coefficients. The random effect is the error
• 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
 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
 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
• 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 nonsignificant 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
• 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
Go to references.
Go to “Other Topics”