How to use HLM 6 for hierarchical linear

How to use HLM 6 for hierarchical linear modeling
(aka “mixed modeling”, aka “generalized estimating equations”)
Use HLM when you have random effects (e.g., outcomes over time, a continuous
variable) nested within fixed effects (e.g., participants, a categorical variable).
Options for the procedure include “PROC MIXED” in SAS, “PROC GLM” with a
“RANDOM” command statement in SAS, “Repeated Measures” under the GLM
menu in SPSS, or the HLM program.
The main disadvantage of using a GLM-based procedure is that it is not able to deal
with missing data – if not all participants have data at all time intervals (especially if
observations are scattered over varying amounts of time or at different intervals for
each person, e.g., in the case of cued diary-type measures), then GLM-based analyses
will drop the time intervals at which not all participants have data (or else drop the
participants who do not have data at all time intervals). This weakness is overcome by
PROC MIXED in SAS (Littell, Milliken, Stroup, & Wolfinger, 1996) or by the HLM
program designed specifically for hierarchical linear modeling (Raudenbush, Bryk,
Cheong, & Congdon, 2001). “The basic theory on which PROC MIXED [in SAS] is
based holds even with unbalanced and missing data, so long as the missing data are
random,” (Littell, et al., 1996). With multiple repeated measures for specific
participants, another issue is that the observations for a given participant are serially
autocorrelated with each other, violating the assumption of independence of
observations which is fundamental to GLM procedures. For these reasons, it is
preferable to use HLM or SAS PROC MIXED when dealing with multiple repeated
measures, rather than the GLM-based Repeated Measures ANOVA option in SPSS.
The basic HLM procedure is not specifically limited by sample size, although some
procedures do require larger samples in order to be reliable (e.g., use of “robust
standard errors” to improve estimates of beta- and gamma-weights in the HLM
program). Assumptions of the procedure include:
• Variables are normally distributed
• Level-2 cases are independent of one another (Level-1 cases are expected to
be dependent)
• There is homogeneity of variance for the variability in the Level-1 cases (the
HLM program has an option to test for whether this assumption is violated)
UCDHSC Center for Nursing Research Updated 5/20/06
Page 1 of 8

STEPS FOR USING HLM:
1. Configure data – Level 1 file has multiple observations per case (change over
time for the case, with a “time” or “sequence” variable, and an
“outcome” variable)
– Level 2 file has only one observation per case (additional
descriptors for the case)
2. Import into HLM program and “make new MDM” file. There are a number of
steps here, and it’s important to do them all in the right order:
— select “stat package input”
— select “HLM2” for the type of analysis (2 levels)
— set “input file type” to “SPSS”
— make up a name for the MDM file (with “.mdm” extension)
— identify the files using “browse” buttons
— use “choose variables” to define the Level 1 & Level 2
variables of interest
— select the variable that is the primary key between the
Level 1 & Level 2 files – it gets flagged as “ID” in both
— if there are any missing data, select “missing data” in the
Level 1 file. If you are using the student version, select
“delete missing data when making MDM” because this
makes the analysis less complex. Otherwise, select “delete
missing data when running analyses,” because this will
conserve statistical power as much as possible.
— click “save mdmt file” and give it a file name.
— click the “make MDM” button.
UCDHSC Center for Nursing Research Updated 5/20/06
Page 2 of 8

3. Click on the “check stats” button to check descriptive stats for each variable:
LEVEL-1 DESCRIPTIVE STATISTICS
VARIABLE NAME N MEAN SD MINIMUM MAXIMUM
SCORE 48 10.00 5.17 1.00 19.00
TRIAL 48 2.50 1.13 1.00 4.00
LEVEL-2 DESCRIPTIVE STATISTICS
VARIABLE NAME N MEAN SD MINIMUM MAXIMUM
ANXIETY 12 1.50 0.52 1.00 2.00
TENSION 12 1.50 0.52 1.00 2.00
4. Click on the “Done” button to go to the next screen
UCDHSC Center for Nursing Research Updated 5/20/06
Page 3 of 8

5. Specify the HLM model – beta coefficients for Level 1 variables; gamma
coefficients for Level 2 variables. Start by specifying the “outcome” variable at
Level 1, then add other variables to the model at Level 1 and Level 2. (Left-click
on each variable name on the list on the left-hand side of the screen, in order to
specify their role in the equation)
6. Clicking either “Basic Settings” or “Outcome” lets you say where to save the
output file, whether to graph results, etc.
7. Save the model, under the “File” menu.
8. Click on “Run Analysis” to see results.
9. “View Output” is under the “file” menu. Results include the model coefficients
and tests for the statistical significance of each predictor. The model also gives
you the level-2 values for each level-1 regression equation:
SAMPLE OUTPUT
Summary of the model specified (in equation format)
---------------------------------------------------
Level-1 Model
Y = B0 + B1*(TRIAL) + R
Level-2 Model
B0 = G00 + U0
B1 = G10 + G11*(ANXIETY) + G12*(TENSION) + U1
UCDHSC Center for Nursing Research Updated 5/20/06
Page 4 of 8

Level-1 OLS regressions
-----------------------
Level-2 Unit INTRCPT1 TRIAL slope
------------------------------------------------------------------------------
1 22.00000 -3.80000
2 23.00000 -4.90000
3 18.00000 -4.00000
4 20.00000 -3.80000
5 15.00000 -3.20000
6 22.50000 -5.60000
7 19.00000 -3.80000
8 21.50000 -5.50000
9 21.00000 -4.80000
10 23.00000 -3.90000
The average OLS level-1 coefficient for INTRCPT1 = 20.12500
The average OLS level-1 coefficient for TRIAL = -4.05000
Least Squares Estimates
-----------------------
sigma_squared = 5.60202
The outcome variable is
SCORE
Least-squares estimates of fixed effects
----------------------------------------------------------------------------
Standard
Fixed Effect Coefficient Error T-ratio d.f. P-value
----------------------------------------------------------------------------
For INTRCPT1, B0
INTRCPT2, G00 20.125000 0.836811 24.050 44 0.000
For TRIAL slope, B1
INTRCPT2, G10 -5.216667 0.611120 -8.536 44 0.000
ANXIETY, G11 0.361111 0.249489 1.447 44 0.155
TENSION, G12 0.416667 0.249489 1.670 44 0.102
----------------------------------------------------------------------------
Interpretation: In this example, the level-2 constant (intercept 2, G00) is a significant
predictor of the level-one constant (beta-zero), which is the participant’s initial level of
performance on the SCORE variable. The level-2 constant (intercept 2, G10) is also a
significant predictor of the level-1 slope (beta-one). Although anxiety level (G11)
UCDHSC Center for Nursing Research Updated 5/20/06
Page 5 of 8

approaches significance (p = .155) as a predictor of beta-one, and tension level (G12) also
approaches significance (p = .102) as a predictor of beta-one, neither of these level-2
predictors had a strong enough effect to be considered statistically significant as a
predictor of the within-person change in the SCORE variable over time (i.e., beta-one).
SAMPLE OUTPUT (CONTINUED)
Final estimation of variance components:
-----------------------------------------------------------------------------
Random Effect Standard Variance df Chi-square P-value
Deviation Component
-----------------------------------------------------------------------------
INTRCPT1, U0 1.87129 3.50174 11 73.95178 0.000
level-1, R 1.56446 2.44754
-----------------------------------------------------------------------------
Interpretation: The level-1 intercept (i.e., people’s starting score) is a significant
predictor of the SCORE variable over time. This means that people are significantly
different from one another (there is variability among the level-1 units), even though the
level-2 predictors weren’t able to account for this variability.
Statistics for current covariance components model
--------------------------------------------------
Deviance = 198.591730
Number of estimated parameters = 2
Interpretation: The deviance statistic is the same as a -2 log likelihood, and the larger it
is, the worse the fit between the model and the data. This -2LL is fairly high (greater than
100), so the model is not an adequate fit for the data. Other predictors or other
combinations of variables should be considered in trying to account for individual
participants’ outcomes on the SCORE variable.
UCDHSC Center for Nursing Research Updated 5/20/06
Page 6 of 8

You can also test one HLM model against another, by using the “hypothesis testing”
command under the “other settings” menu. Just put in this model’s deviance and df (from
the output above), specify and different model, and re-run the analysis to compare them.
One other great new feature in HLM 6 is that you can graph each individual participant’s
level-1 regression line to see the overall pattern and any outliers. Here’s how: use the
“graph equations – level 1 equation graphing” command in the “file” menu.
In the next screen, again select your outcome variable, and the level-1 predictor and
level-2 predictor that you specifically want to focus on. You can select either a subset of
cases (e.g., “first ten cases”) if the sample size is very large, or all cases. In this example
the total n was only 12 cases, so we included all of them.
UCDHSC Center for Nursing Research Updated 5/20/06
Page 7 of 8

The output graph looks like this. It shows you each individual participant’s score (y-axis)
over time (x-axis) as a separate regression line. It further highlights people with the two
different levels of tension (the level-2 predictor) in different colors. This graph confirms
our statistical results, showing that the “tension” variable didn’t significantly differentiate
among people, even though there was a significant association for everyone between
“score” and “time.”
UCDHSC Center for Nursing Research Updated 5/20/06
Page 8 of 8