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Using SAS Proc Mixed to fit the multilevel model for change. Time is nature’s way of keeping everything from happening at once Woody Allen. Judith D. Singer & John B. Willett Harvard Graduate School of Education. Resources to help you learn how to use SAS Proc Mixed.

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using sas proc mixed to fit the multilevel model for change
Using SAS Proc Mixedto fit the multilevel model for change

Time is nature’s way of keeping everything from happening at once

Woody Allen

Judith D. Singer & John B. Willett

Harvard Graduate School of Education

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 1

resources to help you learn how to use sas proc mixed
Resources to help you learn how to use SAS Proc Mixed

Textbook ExamplesApplied Longitudinal Data Analysis: Modeling Change and Event Occurrenceby Judith D. Singer and John B. Willett

Mplus

MLwiN

HLM

SAS

Stata

SPlus

SPSS

Chapter

Datasets

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Table of contents

Ch 1

A framework for investigating change over time

Ch 2

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Exploring longitudinal data on change

Ch 3

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Introducing the multilevel model for change

Ch 4

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Doing data analysis with the multilevel model for change

Ch 5

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Treating time more flexibly

Ch 6

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Modeling discontinuous and nonlinear change

Ch 7

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Examining the multilevel model’s error covariance structure

Ch 8

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Modeling change using covariance structure analysis

Ch 9

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A framework for investigating event occurrence

Ch 10

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Describing discrete-time event occurrence data

Ch 11

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Fitting basic discrete-time hazard models

Ch 12

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Extending the discrete-time hazard model

Ch 13

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Describing continuous-time event occurrence data

Ch 14

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Fitting the Cox regression model

Ch 15

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Extending the Cox regression model

What we’ll do now: Using the specific models we just fit in Chapter Four todemonstrate how to use SAS PROC MIXED to fit these models to data

  • Model A: The unconditional means model
  • Model B: The unconditional growth model
  • Model C: The uncontrolled effects of COA
  • Model D: The controlled effects of COA

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 2

using sas proc mixed to fit model a the unconditional means model
Using SAS Proc Mixed to fit Model A (the unconditional means model)

CompositeModel:

Level-1 Model:

Level-2 Model:

  • The class id statement tells SAS to treat the variable ID as a categorical (in SAS’ terms, a classification) variable. If you omit this statement, by default, SAS would treat ID as a continuous variable.
  • The proc mixed statement invokes the procedure, here using the dataset named “one.”
  • The method = ml option tells SAS to use full maximum likelihood estimation. If you omit this option, by default SAS uses restricted maximum likelihood (as discussed on Chapter 4, slide 27)
  • The covtest option tells SAS to display tests for the variance components. By default, SAS omits these tests (as discussed on Chapter 4, slide 23).

proc mixed data=one method=ml covtest;

class id;

model alcuse = /solution;

random intercept/subject=id;

  • The random statement specifies the stochastic portion of the multilevel model for change. By default, SAS always includes a variance component for the level-1 residuals. In this unconditional means model, the ‘random intercept’ option tells SAS to also include a variance component for the intercept (allowing the means to vary across people).
  • The /subject=id option tells SAS that the intercepts (the means in this unconditional means model) should be allowed to vary randomly across individuals (as identified by the classification variable ID)
  • The model statement specifies the structural portion of the multilevel model for change. This specification ‘model alcuse = ’ may seem unusual but it’s the way SAS represents the unconditional means model (see Chapter 4, slide 9). The model includes no explicit predictor, but like any regression model, includes an implicit intercept by default.
  • The /solution option on the model statement tells SAS to display the estimated fixed effects (as well as the associated standard errors and hypothesis tests).

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 3

results of fitting model a the unconditional means model to data
Results of fitting Model A (the unconditional means model) to data

CompositeModel:

Level-1 Model:

proc mixed data=one method=ml covtest;

class id;

model alcuse = /solution;

random intercept/subject=id;

Level-2 Model:

Model A: Unconditional means model

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

Intercept ID 0.5639 0.1191 4.73 <.0001

Residual 0.5617 0.06203 9.06 <.0001

Fit Statistics

-2 Log Likelihood 670.2

AIC (smaller is better) 676.2

AICC (smaller is better) 676.3

BIC (smaller is better) 683.4

Solution for Fixed Effects

Standard

Effect Estimate Error DF t Value Pr > |t|

Intercept 0.9220 0.09571 81 9.63 <.0001

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 4

using sas proc mixed to fit model b the unconditional growth model
Using SAS Proc Mixed to fit Model B (the unconditional growth model)

Level-1 Model:

Level-2 Model:

CompositeModel:

  • As before, SAS implicitly assumes a variance component for the level-1 residuals. But because Model B includes a second random effect to capture the hypothesized level-2 stochastic variation, the random statement must be modified to include this second term—denoted by the temporal predictor AGE_14.
  • The /type=un, which stands for unstructured, is crucial, telling SAS to not impose any structure on the variance covariance matrix for the level-2 residuals.

proc mixed data=one method=ml covtest;

class id;

model alcuse = age_14/solution;

random intercept age_14/type=un subject=id;

  • Model B, the unconditional growth model, includes a single predictor, age_14, representing the slope of the level-1 individual growth trajectory. As before, SAS implicitly understands that the user wishes to include an intercept term. Because the predictor age_14 is centered at age 14 (the first wave of data collection), the intercept now represents “initial status.”

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 5

results of fitting model b the unconditional growth model to data
Results of fitting Model B (the unconditional growth model) to data

Parameter #1

Parameter #2

proc mixed data=one method=ml covtest;

class id;

model alcuse = age_14/solution;

random intercept age_14/type=un subject=id;

Model B: Unconditional growth model

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(1,1) ID 0.6244 0.1481 4.22 <.0001

UN(2,1) ID -0.06844 0.07008 -0.98 0.3288

UN(2,2) ID 0.1512 0.05647 2.68 0.0037

Residual 0.3373 0.05268 6.40 <.0001

Fit Statistics

-2 Log Likelihood 636.6

AIC (smaller is better) 648.6

AICC (smaller is better) 649.0

BIC (smaller is better) 663.1

Solution for Fixed Effects

Standard

Effect Estimate Error DF t Value Pr > |t|

Intercept 0.6513 0.1051 81 6.20 <.0001

AGE_14 0.2707 0.06245 81 4.33 <.0001

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 6

using sas proc mixed to fit model c uncontrolled effects of coa
Using SAS Proc Mixed to fit Model C (Uncontrolled effects of COA)

Level-1 Model:

Level-2 Model:

CompositeModel:

  • Like the companion Level-2 model, Model C adds two terms to register the uncontrolled effects of COA: (1) a main effect of COA, which captures the effect on the intercept (initial status); and (2) the cross-level interaction, COA*AGE_14, which captures the effect of COA on the rate of change

proc mixed data=one method=ml covtest;

class id;

model alcuse = coa age_14 coa*age_14/solution;

random intercept age_14/type=un subject=id;

  • All other statements, including the random statement, are unchanged from Model B because we have only added new fixed effects (for COA) and not any new random effects.

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 7

results of fitting model c the uncontrolled effects of coa to data
Results of fitting Model C (the uncontrolled effects of COA) to data

proc mixed data=one method=ml covtest;

class id;

model alcuse = coa age_14 coa*age_14/solution;

random intercept age_14/type=un subject=id;

Model C: Uncontrolled effects of COA

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(1,1) ID 0.4876 0.1278 3.81 <.0001

UN(2,1) ID -0.05934 0.06573 -0.90 0.3666

UN(2,2) ID 0.1506 0.05639 2.67 0.0038

Residual 0.3373 0.05268 6.40 <.0001

Fit Statistics

-2 Log Likelihood 621.2

AIC (smaller is better) 637.2

AICC (smaller is better) 637.8

BIC (smaller is better) 656.5

Solution for Fixed Effects

Standard

Effect Estimate Error DF t Value Pr > |t|

Intercept 0.3160 0.1307 80 2.42 0.0179

COA 0.7432 0.1946 82 3.82 0.0003

AGE_14 0.2930 0.08423 80 3.48 0.0008

COA*AGE_14 -0.04943 0.1254 82 -0.39 0.6944

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 8

using sas proc mixed to fit model d controlled effects of coa
Using SAS Proc Mixed to fit Model D (Controlled effects of COA)

Level-1 Model:

Level-2 Model:

CompositeModel:

  • Like the companion Level-2 model, Model D adds two terms to register the controlled effects of PEER: (1) a main effect of PEER, which captures the effect on the intercept (initial status); and (2) the cross-level interaction, PEER*AGE_14, which captures the effect of PEER on the rate of change

proc mixed data=one method=ml covtest;

class id;

model alcuse = coa peer age_14 coa*age_14 peer*age_14/solution;

random intercept age_14/type=un subject=id;

  • All other statements, including the random statement, are unchanged from Model C because we have only added new fixed effects (for PEER) and not any new random effects.

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 9

results of fitting model d the controlled effects of coa to data
Results of fitting Model D (the controlled effects of COA) to data

Model D: Controlled effects of COA

The Mixed Procedure

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

UN(1,1) ID 0.2409 0.09259 2.60 0.0046

UN(2,1) ID -0.00612 0.05500 -0.11 0.9115

UN(2,2) ID 0.1391 0.05481 2.54 0.0056

Residual 0.3373 0.05268 6.40 <.0001

Fit Statistics

-2 Log Likelihood 588.7

AIC (smaller is better) 608.7

AICC (smaller is better) 609.6

BIC (smaller is better) 632.8

Solution for Fixed Effects

Standard

Effect Estimate Error DF t Value Pr > |t|

Intercept -0.3165 0.1481 79 -2.14 0.0356

COA 0.5792 0.1625 82 3.56 0.0006

PEER 0.6943 0.1115 82 6.23 <.0001

AGE_14 0.4294 0.1137 79 3.78 0.0003

COA*AGE_14 -0.01403 0.1248 82 -0.11 0.9107

PEER*AGE_14 -0.1498 0.08564 82 -1.75 0.0840

Go to resources to help you use SAS

© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 10

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© Judith D. Singer & John B. Willett, Harvard Graduate School of Education, Using SAS Proc Mixed, slide 11