SAS Syntax and Output for Data Manipulation: CLDP 944 Example 3a page 1
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1 CLDP 944 Example 3a page 1 From Between-Person to Within-Person Models for Longitudinal Data The models for this example come from Hoffman (2015) chapter 3 example 3a. We will be examining the extent to which a learning achievement outcome) can be predicted from group (control as the reference vs. treatment) and time (pre-test as the reference vs. post-test) in a sample of 50 children. SAS Syntax and Output for Data Manipulation: * Defining global variable for file location to be replaced in code below; %LET filesave= C:\Dropbox\17_CLDP944\CLP944_Example03a; * Location for SAS files for these models (uses macro variable filesave); LIBNAME filesave "&filesave."; * Import and stack chapter 3 two-occasion multivariate data; * Create new variable on left from old variable on right, OUTPUT writes data; DATA work.chapter3a; SET filesave.sas_chapter3a; time=1; outcome=outcome1; OUTPUT; time=2; outcome=outcome2; OUTPUT; DROP outcome1 outcome2; LABEL time = "time: Occasion (1=pre-test, 2=post-test)" outcome = "outcome: Learning Outcome"; RUN; * Center predictors for analysis; DATA work.chapter3a; SET work.chapter3a; time1 = time - 1; treat = group - 1; LABEL time1 = "time1: Time (0=pre-test, 1=post-test)" treat = "treat: Treatment Group (0=control, 1=treatment)"; RUN; * CLASS= means per group and time, WAYS= means overall=0, per category=1, per cell=2; TITLE1 "Chapter 3a Example: Means by group and time for learning outcome"; PROC MEANS MEAN STDERR MIN MAX DATA=work.Chapter3a; CLASS group time; WAYS 0 1 2; VAR outcome; RUN; TITLE1; Cell means by group and time for y outcome Treatment Group Time (1=control, (1=pre-test N 2=treatment) 2=post-test) Obs Mean Std Error Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Marginal means by group for y outcome Treatment Group (1=control, N 2=treatment) Obs Mean Std Error Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Marginal means by time for y outcome Time (1=pre-test N 2=post-test) Obs Mean Std Error Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ Grand mean for y outcome Mean Std Error Minimum Maximum ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
2 CLDP 944 Example 3a page 2 3.1: Between-Person Empty Model TITLE "Eq 3.1: Empty Between-Person model via MIXED"; PROC MIXED DATA=work.Chapter3a NOCLPRINT COVTEST METHOD=REML; MODEL outcome = / SOLUTION DDFM=BW; REPEATED time / R RCORR TYPE=VC SUBJECT=PersonID; RUN; TITLE; Covariance Parameters 1 Columns in X 1 Read 100 Used 100 Not Used This table tells you how many parameters are in your model for the means ( columns in x, the fixed effects, or 1 fixed intercept here) and in your model for the variance ( covariance parameters, or 1 residual variance here). It also tells you how many observations were read per subject, as defined by SUBJECT= on the REPEATED line Cov Z Parm Subject Estimate Error Value Pr > Z time PersonID < Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Solution for Fixed Effects Intercept <.0001 This is the estimate of the residual variance σ. It is labeled time because that is how the R matrix is structured via the REPEATED line. This null model LRT examines the need for any random effects variances and covariances. Because we don t have any (yet), df = 0. This is the estimate of the fixed intercept β. In REML, model df = # for calculating AIC and BIC only includes parameters in the model for the variance.
3 CLDP 944 Example 3a page 3 3.2: Within-Person Empty Model TITLE "Eq 3.2: Empty Within-Person model via MIXED"; PROC MIXED DATA=work.Chapter3a NOCLPRINT COVTEST METHOD=REML; MODEL outcome = / SOLUTION DDFM=BW; REPEATED time / R RCORR TYPE=CS SUBJECT=PersonID; RUN; TITLE; Covariance Parameters 2 Columns in X 1 We still have 1 fixed effect, the fixed intercept, but now the model for the variance includes random intercept variance and residual variance. Read 100 Used 100 Not Used e u u u e u 1 ICC ICC 1 Z Cov Parm Subject Estimate Error Value Pr Z CS PersonID Residual <.0001 CS = Random Intercept Variance τ Residual = Residual Variance σ -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Now we have a random intercept variance, so df=1. This is the model comparison of BP vs. WP. Who wins? Solution for Fixed Effects Intercept <.0001 Which is the better empty model, and how do you know? What is the ICC for these data and what does it mean? Now the model for the variance df=2. This is still the estimate of the fixed intercept β, but note the SE differs.
4 CLDP 944 Example 3a page (top): Between-Person Conditional Model TITLE1 "Eq 3.7 (top): Between-Person Conditional (Predictor) Model via MIXED"; TITLE2 "Not using CLASS statement, manually dummy coding group and time"; PROC MIXED DATA=work.Chapter3a NOCLPRINT COVTEST METHOD=REML; MODEL outcome = time1 treat time1*treat / SOLUTION DDFM=BW; REPEATED time / R RCORR TYPE=VC SUBJECT=PersonID; ESTIMATE "Mean: Control Group at Pre-Test" intercept 1 time1 0 treat 0 time1*treat 0; ESTIMATE "Mean: Control Group at Post-Test" intercept 1 time1 1 treat 0 time1*treat 0; ESTIMATE "Mean: Treatment Group at Pre-Test" intercept 1 time1 0 treat 1 time1*treat 0; ESTIMATE "Mean: Treatment Group at Post-Test" intercept 1 time1 1 treat 1 time1*treat 1; ESTIMATE "Time Effect for Control Group" time1 1 time1*treat 0; ESTIMATE "Time Effect for Treatment Group" time1 1 time1*treat 1; ESTIMATE "Group Effect at Pre-Test" treat 1 time1*treat 0; ESTIMATE "Group Effect at Post-Test" treat 1 time1*treat 1; RUN; TITLE1; TITLE2; Covariance Parameters 1 Columns in X 4 Now we have 4 parameters in the model for the means and 1 parameter in the model for the variance (σ ). Read 100 Used 100 Not Used Cov Z Parm Subject Estimate Error Value Pr > Z time PersonID <.0001 This is the estimate of the residual variance σ. It is labeled time because that is how the R matrix is structured via the REPEATED line. -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) This null model LRT examines the need for any random effects variances and covariances. Because we don t have any (yet), df =
5 CLDP 944 Example 3a page 5 BP Solution for Fixed Effects Intercept <.0001 beta0 time beta1 treat beta2 time1*treat beta3 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F time treat time1*treat Estimates Label Estimate Error DF t Value Pr > t Mean: Control Group at Pre-Test <.0001 Mean: Control Group at Post-Test <.0001 Mean: Treatment Group at Pre-Test <.0001 Mean: Treatment Group at Post-Test <.0001 Time Effect for Control Group beta1 Time Effect for Treatment Group <.0001 beta1 + beta3*1 Group Effect at Pre-Test beta2 Group Effect at Post-Test beta2 + beta3*1 These results assume independent observations what happens if that s not the case? 3.7 (bottom): Within-Person Conditional Model TITLE1 "Eq 3.7 (bottom): Within-Person Conditional (Predictor) Model via MIXED"; TITLE2 "Not using CLASS statement, manually dummy coding group and time"; PROC MIXED DATA=work.Chapter3a NOCLPRINT IC COVTEST METHOD=REML; MODEL outcome = time1 treat time1*treat / SOLUTION DDFM=BW; REPEATED time / R RCORR TYPE=CS SUBJECT=PersonID; ESTIMATE "Mean: Control Group at Pre-Test" intercept 1 time1 0 treat 0 time1*treat 0; ESTIMATE "Mean: Control Group at Post-Test" intercept 1 time1 1 treat 0 time1*treat 0; ESTIMATE "Mean: Treatment Group at Pre-Test" intercept 1 time1 0 treat 1 time1*treat 0; ESTIMATE "Mean: Treatment Group at Post-Test" intercept 1 time1 1 treat 1 time1*treat 1; ESTIMATE "Time Effect for Control Group" time1 1 time1*treat 0; ESTIMATE "Time Effect for Treatment Group" time1 1 time1*treat 1; ESTIMATE "Group Effect at Pre-Test" treat 1 time1*treat 0; ESTIMATE "Group Effect at Post-Test" treat 1 time1*treat 1; RUN; TITLE1; TITLE2; Covariance Parameters 2 Columns in X 4 We still have 4 parameters in the model for the means, but now we have 2 parameters in the model for the variance (τ and σ ). Read 100 Used 100 Not Used 0
6 CLDP 944 Example 3a page e u u u e u 1 ICC ICC 1 Z Cov Parm Subject Estimate Error Value Pr Z CS PersonID <.0001 Residual <.0001 CS = Random Intercept Variance τ Residual = Residual Variance σ -2 Res Log Likelihood AIC (smaller is better) AICC (smaller is better) BIC (smaller is better) Now we have a random intercept variance, so df=1. This is the model comparison of conditional BP vs. WP. Who wins? < WP Solution for Fixed Effects Intercept <.0001 beta0 time <.0001 beta1 treat beta2 time1*treat beta3 Which results differ from the BP model, and why? Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F time <.0001 treat time1*treat Estimates Label Estimate Error DF t Value Pr > t Mean: Control Group at Pre-Test <.0001 Mean: Control Group at Post-Test <.0001 Mean: Treatment Group at Pre-Test <.0001 Mean: Treatment Group at Post-Test <.0001 Time Effect for Control Group <.0001 beta1 Time Effect for Treatment Group <.0001 beta1 + beta3*1 Group Effect at Pre-Test beta2 Group Effect at Post-Test beta2 + beta3*1 What other terms that could possibly be included are missing? Are they really missing?
7 CLDP 944 Example 3a page 7 What if we had used the CLASS statement instead for our conditional within-person model? TITLE1 "Eq 3.7 (bottom): Within-Person Conditional (Predictor) Model via MIXED"; TITLE2 "NOW using CLASS statement"; PROC MIXED DATA=work.Chapter3a NOCLPRINT IC COVTEST METHOD=REML; CLASS PersonID time time1 treat; MODEL outcome = time1 treat time1*treat / SOLUTION DDFM=BW; REPEATED time / R RCORR TYPE=CS SUBJECT=PersonID; LSMEANS time1 treat time1*treat / DIFF=ALL; RUN; TITLE1; TITLE2; Solution for Fixed Effects Time Treatment 1= (0=control, Effect post-test) 1=treatment) Estimate Error DF t Value Pr > t Intercept <.0001 time <.0001 time treat treat time1*treat time1*treat time1*treat time1*treat Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F time <.0001 treat time1*treat Note that the p-values from the solution for fixed effects (simple effects) and Type 3 tests of fixed effects (marginal effects) do not match because they mean different things (stay tuned). Least Squares Means Time Treatment 1= (0=control, Effect post-test) 1=treatment) Estimate Error DF t Value Pr > t time <.0001 time <.0001 treat <.0001 treat <.0001 time1*treat <.0001 time1*treat <.0001 time1*treat <.0001 time1*treat <.0001 Differences of Least Squares Means Time Treatment Time Treatment 1= (0=control, 1= (0=control, Effect post-test) 1=treatment) post-test) 1=treatment) Estimate Error DF t Value Pr > t time <.0001 treat time1*treat time1*treat <.0001 time1*treat <.0001 time1*treat time1*treat <.0001 time1*treat
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