The SAS power analysis Macros for an exponential growth curve model
2009-04-15    Zhang, Z. & Wang, L.
 The SAS Macros for an exponential growth curve model These macros are licensed under the GNL General Public License Version 2.0. You can use/modify/distribute those macros. For questions or comments, please contact Johnny Zhang at zhiyongzhang(@)nd.edu. It would be appreciated if you cite the macros in the following way:Zhang, Z., & Wang, L. (2009). Power analysis for growth curve models using SAS. Behavior Research Methods, 41(4), 1083-1094. Request a copy /*Suppress the output and the log */options nosource nonotes nosource2 nomprint; /*CHANGE THE PARAMETERS HERE*/*model parameters;%LET MuL=10;        *mean peak level;%LET MuS=5;         *mean change between the initial status and the peak level;%LET Sigma_e=1;                 *residual standard deviation;%LET Sigma_L=2;                  *level standard deviation;%LET Sigma_S=.5;            *change standard deviation;%LET rho=0.5;               *correlation between Li and Si;%LET miss=0;        *missing data rate, 0: no missing data;%LET p=1;           *rate of growth/decline;*power parameters;%LET R=10000;        *number of simulation replications;%LET T=6;           *number of measurement occasions;%LET start=100;     *the minimum sample size to consider;%LET end=100;      *the maximum sample size to consider;%LET step=50;       *the step between two sample sizes;%LET df=2;          *the difference in the number of parameters;%LET seed=1;      *random number generator seed; /*DO NOT CHANGE CODES BELOW UNLESS YOU KNOW WHAT YOU ARE DOING*/ /*Calculate the chi-square difference between two nested growth curve models*/%MACRO LL(N,T,seed);DATA Sim_ExpGM;* set statistical parameters;  N = &N; seed = &seed;* setup arrays for repeated measures;  ARRAY y_score{&T} y1-y&T;  ARRAY M{&T} m1-m&T;  m1=1; * generate raw data with considering the missing data rate;  DO _N_ = 1 TO N;    e_L=RANNOR(seed);    e_S=&rho*e_L+SQRT(1-&rho**2)*RANNOR(seed);    L_score=&MuL+&Sigma_L*e_L;    S_score=&MuS+&Sigma_S*e_S;* include indicator variables to generate missing data ;    DO t = 1 TO &T;      y_score{t} = L_score - S_score*exp(-(t-1)*&p) + &Sigma_e*RANNOR(seed);      END; DO t=2 TO &T;   m{t}=m{t-1};   IF m{t-1}=1 AND  RANUNI(seed) > (1-&miss * (t-1))/(1-&miss * (t-2)) THEN m{t} = m{t-1}*0;      IF m{t}=0  THEN y_score{t}=.;   END;    KEEP y1-y&T;    OUTPUT;  END;RUN; DATA ExpGM;  SET Sim_ExpGM;  %DO t = 1 %TO &T;    id = _N_; time=&t-1; y=y&t; OUTPUT;  %END;  KEEP id time y;RUN; /*Fit two nested models to the data*/ODS OUTPUT FitStatistics(persist=proc)=fit;*Model 1: the true model - exponential growth curve model;PROC NLMIXED DATA = ExpGM;  traject = level-slope*exp(-p*(time));  MODEL y ~ NORMAL(traject, v_e);  RANDOM level slope ~ NORMAL([m_l, m_s], [v_l, c_ls, v_s])  SUBJECT = id;  PARMS               m_l = 10  m_s=5 v_l = 4 c_ls = 0.5 v_s = .25 v_e = 1 p=1;RUN; *Model 2: the null model - no variation in Si;PROC NLMIXED DATA = ExpGM;  traject = level-m_s*exp(-p*(time));  MODEL y ~ NORMAL(traject, v_e);  RANDOM level ~ NORMAL(m_l, v_l)  SUBJECT = id;  PARMS               m_l = 10  m_s=5  v_l = 4                v_e = 1 p=1;RUN;ODS OUTPUT CLOSE;%MEND LL; /*The second Macro: POWER*//*This Macro calls the first Macro LL for each replication*/* Calculate power based on R replications;%MACRO POWER(R,N,T,seed,df);DATA tempfit;  DO _N_=1 TO 8;    tempfit=_N_; OUTPUT;  END;RUN;  %LL(&N,&T,&seed);DATA fit;  MERGE fit tempfit;RUN; DATA allfit;  SET fit;RUN; %DO I = 2 %TO  &R;  PROC DATASETS LIBRARY=WORK; DELETE fit; RUN; QUIT;  %LL(&N,&T,%eval(&seed+&I*1389));  DATA fit;    MERGE fit tempfit;  RUN;   DATA allfit;    SET allfit fit;  RUN;  DM 'CLEAR LOG';%END; DATA allfit;  SET allfit;  IF MOD(_N_,4) ~= 1 THEN DELETE;  KEEP Value;RUN; DATA allfit;  SET allfit;  id =INT((_N_-.1)/2)+1;  modelnum = MOD(_N_+1, 2);RUN; PROC TRANSPOSE DATA=allfit OUT=allfit prefix=model;  BY id;  ID modelnum;  VAR Value;RUN; DATA allfit;  SET allfit;  ss = &N;  diff = model1 - model0;  ind = 1;  IF diff=. THEN DELETE;  IF diff<0 THEN DELETE;  IF diff < CINV(.95, &df) THEN ind = 0;  DROP id _NAME_ model0 model1;RUN; PROC MEANS DATA = allfit;  VAR ss ind;  OUTPUT OUT=power mean(ss ind)=ss power;RUN; %MEND POWER;*%POWER(&R, 100, &T, &seed, &df);/*The third Macro: POWERCURVE*//* This Macro calls the second Macro for each sample size*/%MACRO powercurve(R, seed, st, end, step, T,df);%POWER(&R, &st, &T, %eval(&seed+&st), &df);DATA allpower;  SET power;  RUN; %LET st = %eval(&st + &step);%DO %WHILE (&st <=  &end);  %POWER(&R, &st, &T, %eval(&seed+&st), &df);  %LET st = %eval(&st + &step);   DATA allpower;    SET allpower power;  RUN;  DM 'CLEAR LOG';%END; * Save the results for possible future use;DATA allpower;  SET allpower;  FILE "power-exp-new.txt";  PUT _FREQ_ ss power;RUN; * Plot the power curve;ODS PDF FILE='power.pdf' NOTOC;PROC GPLOT DATA = allpower;  SYMBOL I=JOIN;  PLOT power*ss;RUN;QUIT;ODS PDF CLOSE;%MEND powercurve; ODS RESULTS OFF;ODS LISTING CLOSE;%powercurve(&R,&seed,&start,&end,&step,&T,&df);ODS RESULTS ON;ODS LISTING;
Editor: johnny