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TVEM_Mix_Normal_OldVersion.sas
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TVEM_Mix_Normal_OldVersion.sas
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%MACRO TVEM_Mix_Normal( MyData,
Time,
Dep,
ID,
Latent_Classes,
Cov=,
SCov=,
TCov=,
Knots=,
Num_Starts=5,
Convergence=1e-8 ,
Coverage=0.95 ,
Deg=2,
Equal_Variance=no,
Gamma_Prior_Strength=0,
Initial_Seed=100000,
Max_Iterations=5000,
Max_Variance_Ratio=10,
Mesh=20,
Penalty_Max=.,
Ref=1,
Scale=500,
Std_Err_Option=yes,
Use_Roughness_Penalty=yes);
/***************************************************************
| MixTVEM macro Version 1.1
| By John DZIAK, Xianming TAN, and Runze LI
| Fits a mixture of nonparametric trajectories to longitudinal data.
|
| Copyright:
| (c) 2013 The Pennsylvania State University
|
| License:
| This program is free software; you can redistribute it and/or
| modify it under the terms of the GNU General Public License as
| published by the Free Software Foundation; either version 2 of
| the License, or (at your option) any later version.
|
| This program is distributed in the hope that it will be useful,
| but WITHOUT ANY WARRANTY; without even the implied warranty of
| MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
| General Public License for more details.
|
| Acknowledgments and references:
| We fit a mixture of nonparametric varying-coefficient models, using
| a penalized B-spline approach. See
| de Boor, C. (1977). Package for calculating with B-splines.
| SIAM Journal on Numerical Analysis, 14, 441-72.
| Eilers, P.H.C. and Marx, B.D. (1996). Flexible smoothing using
| B-splines and penalized likelihood. Statistical Science
| 11(2): 89-121.
| Hastie, T., & Tibshirani, R. (1993). Varying-coefficient models. Journal
| of the Royal Statistical Society, Series B, 55, 757-796.
| Shiyko, M. P., Lanza, S. T., Tan, X., Li, R., Shiffman, S. (2012). Using
| the Time-Varying Effect Model (TVEM) to Examine Dynamic Associations
| between Negative Affect and Self Confidence on Smoking Urges:
| Differences between Successful Quitters and Relapsers. Prevention
| Science, 13, 288-299.
| Ramsay, J., Hooker, G., & Graves, S. (2009). Functional Data Analysis with
| R and MATLAB. New York: Springer.
| Tan, X., Shiyko, M. P., Li, R., Li, Y., & Dierker, L. (2011, November 21).
| A time-varying effect model for intensive longitudinal data.
| Psychological Methods. Advance online publication. doi: 10.1037/a0025814.
| Estimation is done using the EM algorithm for finite mixtures.
| McLachlan, G. J., and Peel, D. (2000). Finite mixture models. New York: Wiley.
| Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood
| from incomplete data via the EM algorithm. Journal of the Royal
| Statistical Society, B, 39, 1-38.
| The standard error calculations for the mixture approach are based on
| those used by Turner (2000) and Turner's mixreg R package, which are based on the
| ideas of Louis (1982).
| Louis, T. A. (1982). Finding the Observed Information Matrix when Using
| the EM Algorithm. Journal of the Royal Statistical Society, B, 44, 226-233.
| Turner, T. R. (2000) Estimating the rate of spread of a viral infection of
| potato plants via mixtures of regressions. Applied Statistics, 49,
| pp. 371-384.
| Turner, R. (2009). mixreg: Functions to fit mixtures of regressions.
| R package version 0.0-3. http://CRAN.R-project.org/package=mixreg
| The use of a sandwich formula to adjust for within-subject correlation
| when calculating the standard errors is inspired by
| Liang, K.-Y., and Zeger, S. L. (1986). Longitudinal data analysis
| using generalized linear models. Biometrika, 73, 13-22.
| Clustering functional data modeled with splines is described in
| James, G., and Sugar, C. (2003) Clustering for sparsely sampled
| functional data. Journal of the American Statistical
| Association 98, 397-408.
| Some web resources which were helpful in writing this macro:
| SAS FAQ: How can I recode my ID variable to be short and numeric?.
| UCLA: Academic Technology Services, Statistical Consulting Group.
| Accessed at http://www.ats.ucla.edu/stat/sas/faq/enumerate_id.htm.
| Accessed Feb. 22, 2012 (and before).
| Statistical Computing Seminar: Proc Logistic and Logistic Regression Models.
| UCLA: Academic Technology Services, Statistical Consulting Group.
| Accessed at http://www.ats.ucla.edu/stat/sas/seminars/sas_logistic/logistic1.htm.
| Accessed Feb. 22, 2012 (and before).
| Deng, C. Q. (June 27, 2009). Spaghetti plot. Blog entry on "On Biostatistics
| and Clinical Trials: CQ's web blog on the issues in biostatistics and
| clinical trials." Accessed at
| http://onbiostatistics.blogspot.com/2009/06/spaghetti-plot.html.
| Some of the code is adapted from the TVEM macro suite:
| TVEM SAS Macro Suite (Version 2.1.0) [Software]. (2012). University
| Park: The Methodology Center, Penn State.
| Retrieved from http://methodology.psu.edu.
| Yang, J., Tan, X., Li, R., & Wagner, A. (2012). TVEM (time-varying
| effect model) SAS macro suite users' guide (Version 2.1.0). University
| Park: The Methodology Center, Penn State.
| Retrieved from http://methodology.psu.edu.
| The optional gamma stabilization prior is similar to that used
| in Latent GOLD and PROC LCA. See
| Lanza, S. T., Dziak, J. J., Huang, L., Xu, S., & Collins, L. M. (2011).
| PROC LCA & PROC LTA users' guide (Version 1.2.7). University Park: The
| Methodology Center, Penn State. Retrieved from http://methodology.psu.edu.
| Chung, H., Flaherty, B. P., and Schafer, J. L. (2006). Latent class
| logistic regression: application to marijuana use and attitudes
| among high school seniors. Journal of the Royal Statitical
| Society, A, 169, 723-743.
| Clogg, C. C. and Goodman, L. A. (1984) Latent structure analysis of a
| set of multidimensional contingency tables. JASA, 79, 762–771.
| The model fit criteria used are adapted versions of the standard AIC, BIC
| and GCV of:
| Akaike, H. (1973). Information theory and an extension of the maximum
| likelihood principle. In B. N. Petrov & F. Csaki (Eds.), Second
| international symposium on information theory (p. 267-281).
| Budapest, Hungary: Akademai Kiado.
| Schwarz, G. (1978). Estimating the dimension of a model. Annals of
| Statistics, 6, 461-464.
| Craven, P., and Wahba, G. (1978). Smoothing noisy data with spline
| functions: Estimating the correct degree of smoothing by the
| method of generalized cross-validation. Numerische
| Mathematik, 31, 377–403.
/***************************************************************/
OPTIONS NONOTES;
%LET MixTVEMDebug = 0;
%LET SEIgnoreInfoLoss=0; /* don't try to make calculations faster by leaving I2 matrix at zero */
/* First process the user input values. If these trigger an error
right away (i.e., they appear to be un-implementable or nonsensical)
then we don't do anything else. This part of the code goes through
the user-provided input arguments
and checks whether the values are unreasonable or impossible. If
it finds impossible values, it gives an error message. Otherwise,
the checked input values are processed and saved in new macro
variables and in a dataset named MixTVEMSettings. */
PROC IML;
MacroError = 0;
/* MyData */
MyData= "&MyData";
IF (LENGTH("_%TRIM(&MyData)")<2) THEN DO;
PRINT("Error -- The input dataset name must be provided.");
MacroError=1;
END;
/* Time */
Time = "&Time";
IF (LENGTH("_%TRIM(&Time)")<2) THEN DO;
PRINT("Error -- The time variable name must be provided.");
MacroError=1;
END;
IF (LENGTH("_%TRIM(&Time)")>25) THEN DO;
PRINT("Error -- The time variable name is too long.");
MacroError=1;
END;
/* Dep */
Dep = "&Dep";
IF (LENGTH("_%TRIM(&Dep)")<2) THEN DO;
PRINT("Error -- The response variable name must be provided.");
MacroError=1;
END;
/* ID */
ID = "&ID";
IF (LENGTH("_%TRIM(&ID)")<2) THEN DO;
PRINT("Error -- The subject ID variable name must be provided.");
MacroError=1;
END;
/* Latent_Classes */
IF (LENGTH("_%TRIM(&Latent_Classes)")<2) THEN DO;
PRINT("Error -- The number of classes must be provided.");
MacroError=1;
END;
NumClasses = &Latent_Classes;
IF (NumClasses < 1) THEN DO;
PRINT("Error -- There must be at least one class.");
MacroError = 1;
END;
IF (NumClasses > 19) THEN DO;
PRINT("Error -- Cannot fit that many classes.");
MacroError = 1;
END;
%GLOBAL MixTVEMNumClasses;
CALL SYMPUT("MixTVEMNumClasses",CHAR(NumClasses));
/* Ref */
IF (LENGTH("_%TRIM(&Ref)")<2) THEN RefClass = .;
ELSE RefClass = &Ref;
IF (RefClass < 1) THEN DO;
PRINT("Error -- Ref must be at least 1.");
MacroError = 1;
END;
IF (RefClass > NumClasses) THEN DO;
PRINT("Error -- Ref cannot be greater than the number of classes.");
MacroError = 1;
END;
/* Cov */
CovInput = " &Cov"; /* note the trailing space; it makes things work*/
Cov = TRANSLATE(STRIP(COMPBL(CovInput))," ",",");
IF Cov ="" THEN NumCov = 0; ELSE NumCov = 1 + COUNT(Cov," ");
%GLOBAL MixTVEMNumCov;
CALL SYMPUT("MixTVEMNumCov",CHAR(NumCov));
%GLOBAL MixTVEMCov;
IF NumCov>0 THEN DO;
CALL SYMPUT("MixTVEMCov",Cov);
END; ELSE DO;
CALL SYMPUT("MixTVEMCov","DummyPlaceholder");
END;
IF Cov ="" THEN Cov = .;
/* SCov */
SCovInput = " &SCov"; /* note the trailing space; it makes things work*/
SCov = TRANSLATE(STRIP(COMPBL(SCovInput))," ",",");
IF SCov ="" THEN NumSCov = 0; ELSE NumSCov = 1 + COUNT(SCov," ");
%GLOBAL MixTVEMNumSCov;
CALL SYMPUT("MixTVEMNumSCov",CHAR(NumSCov));
%GLOBAL MixTVEMSCov;
IF SCov ="" THEN SCov = .;
IF NumSCov>0 THEN DO;
CALL SYMPUT("MixTVEMSCov",SCov);
END; ELSE DO;
CALL SYMPUT("MixTVEMSCov","DummyPlaceholder");
END;
/* TCov */
TCovInput = " &TCov"; /* note the trailing space; it makes things work*/
TCov = TRANSLATE(STRIP(COMPBL(TCovInput))," ",",");
IF TCov ="" THEN NumTCov = 0; ELSE NumTCov = 1 + COUNT(TCov," ");
%GLOBAL MixTVEMNumTCov;
CALL SYMPUT("MixTVEMNumTCov",CHAR(NumTCov));
%GLOBAL MixTVEMTCov;
IF NumTCov>0 THEN DO;
CALL SYMPUT("MixTVEMTCov",TCov);
END; ELSE DO;
CALL SYMPUT("MixTVEMTCov","DummyPlaceholder");
END;
IF TCov ="" THEN TCov = .;
/* Knots */
Knots= "&Knots";
IF (NumTCov>0) THEN DO;
IF (LENGTH("_%TRIM(&Knots)")<2) THEN DO;
PRINT("Error -- Knot information must be provided.");
MacroError = 1;
END;
/* Have to create dataset of knots */
USE &MyData;
READ ALL VAR {&Time} INTO Time;
CLOSE &MyData;
KnotsString = TRANSLATE("'&Knots'"," ",",");
CALL SYMPUT("MixTVEMTemp",KnotsString);
NumKnotsVec = {. &Knots}`; /* The extra entry is here to prevent a macro error */
NumKnotsVec=NumKnotsVec[2:NROW(NumKnotsVec)];
IF NumKnotsVec[><]<1 THEN DO;
PRINT ("Error -- Please use at least one knot per time-varying coefficient.");
MacroError = 1;
END;
StartTime = Time[><];
StopTime = Time[<>];
IF (NumTCov^=NROW(NumKnotsVec)) THEN DO;
PRINT ("Error -- Please check the knots string.");
MacroError = 1;
END;
InteriorKnotsMatrix = J(NumKnotsVec[<>],NumTCov,.);
DO k = 1 TO NumTCov;
IF NumKnotsVec[k]>0 THEN DO;
InteriorKnotsMatrix[1:NumKnotsVec[k],k] = (StartTime + ((1:NumKnotsVec[k]))*
(StopTime-StartTime)/(NumKnotsVec[k]+1))`;
END;
END;
CREATE MixTVEMInteriorKnotsMatrix FROM InteriorKnotsMatrix;
APPEND FROM InteriorKnotsMatrix;
CLOSE MixTVEMInteriorKnotsMatrix;
KnotsDatasetName = "MixTVEMInteriorKnotsMatrix";
END;
/* Deg */
IF (LENGTH("_%TRIM(&Deg)")<2) THEN Deg = .;
Deg = &Deg;
IF (Deg = .) THEN DO;
Deg = 1;
END;
IF (^((Deg=1)|(Deg=2)|(Deg=3))) THEN DO;
PRINT("Error -- Cannot fit that order of penalized spline.");
MacroError = 1;
END;
/* Standard error option */
StdErrOptionInput = "&Std_Err_Option";
IF ( SUBSTR(UPCASE(STRIP(StdErrOptionInput )),1,1) = "Y" |
SUBSTR(UPCASE(STRIP(StdErrOptionInput )),1,1) = "S" |
SUBSTR(UPCASE(STRIP(StdErrOptionInput )),1,1) = "1" ) THEN DO;
StdErrOption= 1;
END; ELSE IF ( SUBSTR(UPCASE(STRIP(StdErrOptionInput )),1,1) = "N" |
SUBSTR(UPCASE(STRIP(StdErrOptionInput )),1,1) = "0" ) THEN DO;
StdErrOption= 0;
END;
ELSE DO;
PRINT("Error -- Please provide yes or no for Std_Err_Option.");
MacroError = 1;
END;
IF (^((StdErrOption=0)|(StdErrOption=1))) THEN DO;
PRINT("Error -- This standard error option is not currently supported.");
MacroError = 1;
END;
/* Equal_Variance */
EqualVarianceInput = "&Equal_Variance";
IF ( SUBSTR(UPCASE(STRIP(EqualVarianceInput)),1,1) = "Y" |
SUBSTR(UPCASE(STRIP(EqualVarianceInput)),1,1) = "1" ) THEN DO;
EqualVariance = 1;
END; ELSE IF ( SUBSTR(UPCASE(STRIP(EqualVarianceInput)),1,1) = "N" |
SUBSTR(UPCASE(STRIP(EqualVarianceInput)),1,1) = "0" ) THEN DO;
EqualVariance = 0;
END; ELSE DO;
PRINT("Error -- Please provide yes or no for Equal_Variance.");
EqualVariance = 1;
MacroError = 1;
END;
/* Coverage */
/* "Coverage" here means nominal coverage. It is not to be taken too
literally, because the confidence intervals which are constructed are
only pointwise intervals and not a familywise confidence band for the
whole curve, and because the confidence intervals are conditional on
the regression model being correct (e.g., knots are in the right place,
response is normal with variance not a function of time). In reality
these assumptions will be at least slightly inaccurate. Also,
concerns about under-coverage of the sandwich matrix (see Kauermann
and Carroll (2001, JASA) should be considered.*/
IF (LENGTH("_%TRIM(&Coverage)")<2) THEN DO;
Coverage = .95;
END; ELSE DO;
Coverage = &Coverage;
IF (Coverage < 0.50) THEN DO;
PRINT("Error -- The specified coverage level is too low.");
MacroError = 1;
END;
IF (Coverage > 0.99999) THEN DO;
PRINT("Error -- The specified coverage level is too high.");
MacroError = 1;
END;
END;
/* Convergence */
IF (LENGTH("_%TRIM(&Convergence)")<2) THEN DO;
Convergence = 1e-8;
END; ELSE DO;
Convergence = &Convergence;
IF (Convergence < 1e-15) THEN DO;
PRINT("Error -- The specified convergence criterion is too small.");
MacroError = 1;
END;
IF (Convergence > 1e-4) THEN DO;
PRINT("Error -- The specified convergence criterion is too large.");
MacroError = 1;
END;
END;
/* MaxIterations */
MaxIterations = &Max_Iterations;
IF (MaxIterations < 50) THEN DO;
PRINT("Error -- The specified maximum number of iterations is too small.");
MacroError = 1;
END;
/* Max_Variance_Ratio */
MaxVarianceRatio = &Max_Variance_Ratio;
IF (MaxVarianceRatio = .) THEN MaxVarianceRatio = 1000;
IF (MaxVarianceRatio < 0) THEN DO;
PRINT("Error -- The value supplied for Max_Variance_Ratio should not be negative.");
MacroError = 1;
END;
/* Gamma_Prior_Strength */
GammaStabilizingConstant = &Gamma_Prior_Strength;
IF (GammaStabilizingConstant = .) THEN GammaStabilizingConstant = 0;
IF (GammaStabilizingConstant < 0) THEN DO;
PRINT("Error -- The value supplied for Gamma_Prior_Strength should not be negative.");
MacroError = 1;
END;
/* Use_Roughness_Penalty */
RoughnessPenalty = 0;
UseRoughnessPenaltyInput = "&Use_Roughness_Penalty";
IF ( SUBSTR(UPCASE(STRIP(UseRoughnessPenaltyInput)),1,1) = "Y" |
SUBSTR(UPCASE(STRIP(UseRoughnessPenaltyInput)),1,1) = "1" ) THEN DO;
UseRoughnessPenalty = 1;
END; ELSE IF ( SUBSTR(UPCASE(STRIP(UseRoughnessPenaltyInput)),1,1) = "N" |
SUBSTR(UPCASE(STRIP(UseRoughnessPenaltyInput)),1,1) = "0" ) THEN DO;
UseRoughnessPenalty = 0;
END; ELSE DO;
PRINT("Error -- Please provide yes or no for Use_Roughness_Penalty.");
UseRoughnessPenalty = 0;
MacroError = 1;
END;
/* Mesh */
Mesh = &Mesh;
IF (Mesh < 2) THEN DO;
PRINT("Error -- The value supplied for Mesh should be greater than 1.");
MacroError = 1;
END;
/* Penalty_Max */
Penalty_Max = &Penalty_Max;
IF ((Penalty_Max < 0)&(Penalty_Max ^= .)) THEN DO;
PRINT("Error -- The value supplied for Penalty_Max should not be negative.");
MacroError = 1;
END;
/* Scale */
ScaleForGraph = &Scale;
IF (ScaleForGraph < 0) THEN DO;
PRINT("Error -- The value supplied for Scale should not be negative.");
MacroError = 1;
END;
/* Initial_Seed */
IF (LENGTH("_%TRIM(&Initial_Seed)")<2) THEN DO;
InitialSeed = .;
END;
InitialSeed = &Initial_Seed;
IF (InitialSeed = .) THEN DO;
InitialSeed = 0;
END;
IF (InitialSeed < 0) THEN DO;
PRINT("Error -- Need a nonnegative random seed.");
MacroError = 1;
END;
SelectedSeed = .;
/* Num_Starts */
IF (LENGTH("_%TRIM(&Num_Starts)")<2) THEN DO;
PRINT("Error -- The number of starting values must be provided.");
MacroError=1;
END;
NumStarts = &Num_Starts;
IF (NumStarts < 1) THEN DO;
PRINT("Error -- There must be at least one starting value.");
MacroError = 1;
END;
IF ((NumStarts=1)&(InitialSeed=0)) THEN DO;
PRINT("Error -- Please either specify a higher Num_Starts or a nonzero Initial_Seed.");
MacroError = 1;
END;
Iterations = .; /* Not filled in until later */
CREATE MixTVEMSettings VAR {
Convergence
Cov
Coverage
Deg
Dep
EqualVariance
GammaStabilizingConstant
ID
InitialSeed
Iterations
Knots
MacroError
MaxIterations
MaxVarianceRatio
Mesh
NumClasses
NumCov
NumSCov
NumStarts
NumTCov
Penalty_Max
RefClass
RoughnessPenalty
ScaleForGraph
SCov
StdErrOption
Tcov
UseRoughnessPenalty };
APPEND;
CLOSE MixTVEMSettings;
QUIT;
DATA MixTVEMData;
SET &MyData;
KEEP &ID &Time
%IF %EVAL(&MixTVEMNumCov>0) %THEN %DO; &MixTVEMCov %END;
%IF %EVAL(&MixTVEMNumSCov>0) %THEN %DO; &MixTVEMSCov %END;
%IF %EVAL(&MixTVEMNumTCov>0) %THEN %DO; &MixTVEMTCov %END;
&Dep;
WHERE ((&ID IS NOT MISSING) &
(&Time IS NOT MISSING) &
%DO MixTVEMThisVarIndex = 1 %TO &MixTVEMNumCov;
(%QSCAN(&MixTVEMCov,&MixTVEMThisVarIndex," ") IS NOT MISSING) &
%END;
%DO MixTVEMThisVarIndex = 1 %TO &MixTVEMNumSCov;
(%QSCAN(&MixTVEMSCov,&MixTVEMThisVarIndex," ") IS NOT MISSING) &
%END;
%DO MixTVEMThisVarIndex = 1 %TO &MixTVEMNumTCov;
(%QSCAN(&MixTVEMTCov,&MixTVEMThisVarIndex," ") IS NOT MISSING) &
%END;
(&Dep ^= .));
RUN;
PROC IML;
USE MixTVEMData; READ ALL INTO MixTVEMData; CLOSE MixTVEMData;
USE MixTVEMSettings; READ VAR {EqualVariance
GammaStabilizingConstant
InitialSeed
MacroError
MaxIterations
NumStarts
StdErrOption };
CLOSE MixTVEMSettings;
%GLOBAL MixTVEMEqualVariance; CALL SYMPUT("MixTVEMEqualVariance",CHAR(EqualVariance));
%GLOBAL MixTVEMGammaStrength; CALL SYMPUT("MixTVEMGammaStrength",CHAR(GammaStabilizingConstant));
%GLOBAL MixTVEMInitialSeed; CALL SYMPUT("MixTVEMInitialSeed",CHAR(InitialSeed));
%GLOBAL MixTVEMMacroError; CALL SYMPUT("MixTVEMMacroError",CHAR(MacroError));
%GLOBAL MixTVEMMaxIterations; CALL SYMPUT("MixTVEMMaxIterations",CHAR(MaxIterations));
%GLOBAL MixTVEMNumStarts; CALL SYMPUT("MixTVEMNumStarts",CHAR(NumStarts));
%GLOBAL MixTVEMNumTotal; CALL SYMPUT("MixTVEMNumTotal",CHAR(NROW(MixTVEMData)));
%GLOBAL MixTVEMStdErrOption; CALL SYMPUT("MixTVEMStdErrOption",CHAR(StdErrOption));
QUIT;
PROC SORT DATA=MixTVEMData TAGSORT NOTHREADS;
BY &ID;
RUN;
DATA MixTVEMData; SET MixTVEMData;
BY &ID;
RETAIN MixTVEMIntID 0;
IF first.&ID THEN MixTVEMIntID = MixTVEMIntID + 1;
/* This creates a recoded version of the subject ID variable,
called "MixTVEMIntID," that is composed of consecutive
integers starting with 1. This makes it possible for some
of the code in the macro to be simpler than if subjects could
have anything for ID's.
See http://www.ats.ucla.edu/stat/sas/faq/enumerate_id.htm; */
OUTPUT;
%GLOBAL MixTVEMNumSubjects;
CALL SYMPUT("MixTVEMNumSubjects",MixTVEMIntID);
RUN;
DATA MixTVEMSettings;
SET MixTVEMSettings;
NumTotal = &MixTVEMNumTotal;
NumSubjects = &MixTVEMNumSubjects;
IF (Penalty_Max = .) THEN Penalty_Max = NumTotal;
RUN;
/* Now create a datafile, MixTVEMSBySub, which contains
the S predictors if there are any. Unlike MixTVEMData and MixTVEMDataX,
which have one record per observation, this dataset will be much smaller,
having only one record per subject. This is because class membership is
considered to be a stable characteristic that does not change. Thus, its
predictors in the model are not expected to be time-varying either. */
%IF %EVAL(&MixTVEMDebug>0) %THEN %PUT Now prepare subject variables matrix;
PROC IML;
USE MixTVEMSettings;
READ VAR{ NumSCov } INTO NumSCov ;
READ VAR{ SCov } INTO SCov ;
READ VAR{ NumSubjects } INTO NumSubjects ;
READ VAR{ NumTotal } INTO NumTotal ;
READ VAR{ MacroError} INTO MacroError;
CLOSE MixTVEMSettings;
USE MixTVEMData;
READ ALL VAR{MixTVEMIntID} INTO IntID;
CLOSE MixTVEMData;
AvailableCov = CONTENTS(MixTVEMData) ;
SCovArray = "Intercept";
IF NumSCov>0 THEN DO;
DO i = 1 TO NumSCov;
ThisVariable = SCANQ(SCov,i);
VarFound = (COMPARE(ThisVariable,AvailableCov,"li")=0)[+];
IF VarFound = 0 THEN DO;
PRINT "Error -- Could not find this variable in the dataset:" ThisVariable;
MacroError = 1;
END;
IF (COMPARE(ThisVariable,"Intercept","li")=0) THEN DO;
PRINT("Error -- An intercept variable should not be included in the S variables.");
MacroError = 1;
/* The user should not have provided an intercept column for S,
since one will be provided automatically and we do not want
redundant columns. */
END;
SCovArray = SCovArray // ThisVariable;
END;
USE MixTVEMData; READ ALL VAR {&MixTVEMSCov} INTO SCov ; CLOSE MixTVEMSCov ;
IF (((SCov[<>]=SCov[><])[+])>0) THEN DO;
PRINT("Error -- An intercept or constant column should not be included in the S variables.");
MacroError = 1;
END;
IF (NROW(SCov)^=NumTotal) THEN DO;
PRINT("Error -- Unexpected amount of data in S variables.");
MacroError = 1;
END;
SByObs = J(NumTotal,1,1) || SCov;
END; ELSE DO;
SByObs = J(NumTotal,1,1);
END;
SNum = (1:(NumSCov+1))`;
SCovName = SCovArray;
CREATE MixTVEMSCovNames VAR{SNum SCovName};
APPEND;
CLOSE MixTVEMSCovNames;
IF (NROW(SByObs) ^= NumTotal)|(NCOL(SByObs) ^= NumSCov+1) THEN DO;
PRINT("Error -- Unexpected amount of data in S variables.");
MacroError = 1;
END;
IF (NROW(IntID) ^= NumTotal)|(NCOL(IntID) ^= 1) THEN DO;
PRINT("Error -- Unexpected amount of data in ID variable.");
MacroError = 1;
END;
IF (IntID[><] ^= 1)|(IntID[<>]^=NumSubjects) THEN DO;
PRINT("Error -- Unexpected values of data in ID variable.");
MacroError = 1;
END;
SBySub = J(NumSubjects,NCOL(SByObs),0);
ThisRowOkayForThisSubject = J(NumTotal,1,0);
sub = 1;
SBySub[sub,] = SByObs[1,];
GaveErrorMessage = 0;
/* The following loop is somewhat tricky but involves compressing
the dataset which the user provides (which has NumTotal rows,
one for each observation on each subject), into a new dataset
with NumSubject rows (having only NumSubject rows, i.e., one row
for each subject, where NumSubject is less than or equal to NumTotal.)
The loop also checks to try to make sure that this is meaningful and
does not cause confusion due to misspecified ID or S variables. In other
words, the subjects in MixTVEMData should have a one-to-one mapping
onto the subjects in MixTVEMSBySub, and the observations in MixTVEMData
should have a many-to-one mapping to the values in MixTVEMData.*/
DO obs = 2 TO NumTotal;
IF IntID[obs]<IntID[obs-1] THEN DO;
PRINT("Error -- Possible bug -- Internal ID variable not sorted.");
MacroError = 1;
END;
IF IntID[obs]>IntID[obs-1] THEN DO;
/* Start new subject */
sub = sub + 1;
SBySub[sub,] = SByObs[obs,];
END; ELSE DO;
/* Continuing old subject. Check to make sure that the S variables
are constant within-subject. */
IF SBySub[sub,] ^= SByObs[obs,] THEN DO;
IF (GaveErrorMessage=0) THEN DO;
PRINT("Error -- The S variables do not appear to be constant within subject.");
PRINT "Check observation # " obs " and subject # " sub "in the dataset.";
GaveErrorMessage = 1;
END;
MacroError = 1;
END;
END;
END;
IF((SBySub[<>,]=SBySub[><,])[+]>1) THEN DO;
PRINT("Error -- One of the S variables (not the intercept) seems to be a constant.");
MacroError = 1;
END;
IF(NCOL(SBySub)^=NROW(SCovArray)) THEN DO;
PRINT("Error -- Difficulty deciding number of S variable columns.");
MacroError = 1;
END;
IF MacroError>0 THEN DO;
EDIT MixTVEMSettings VAR{MacroError}; MacroError = MacroError; REPLACE; CLOSE MixTVEMSettings;
END;
CREATE MixTVEMSBySub FROM SBySub [ COLNAME = SCovArray ]; APPEND FROM SBySub; CLOSE MixTVEMSBySub;
QUIT;
%IF %EVAL(&MixTVEMDebug>0) %THEN %PUT Finished preparing S matrix;
%IF %EVAL(&MixTVEMDebug>0) %THEN %PUT Now prepare random seeds;
DATA MixTVEMRandomSeeds;
DO SeedID = 1 TO &MixTVEMNumStarts;
Seeds = ROUND(RANUNI(&MixTVEMInitialSeed)*1000000);
HardRSS = .;
WeightedRSS = .;
LogLik = .;
SmallestPrevalence = .;
LargestPrevalence = .;
OUTPUT;
END;
RUN;
%IF %EVAL(&MixTVEMDebug>0) %THEN %PUT Finished preparing random seeds;
PROC IML;
%IF %EVAL(&MixTVEMDebug>0) %THEN %PUT Start preparing regressor matrix;
START my_Bspline(x, knots, d);
/* evaluate the values of (num of knots) + d +1 B-spline basis functions at x, x is a real number*/
/* output a vector of (num of knots) + 1 - d real numbers */
/* knots include both exterior and inner knots */
n_ext = ncol(knots);
all_knots = (1:(n_ext+2));
all_knots[1] = knots[1] - (1e-12);
all_knots[2:(n_ext+1)]= knots;
all_knots[n_ext+2] = knots[n_ext] + (1e-12);
n_ext =n_ext+2;
tmp=0.0*(1:(n_ext-1));
DO i = 1 TO (n_ext-1);
IF (x>=all_knots[i] & x<all_knots[i+1]) THEN tmp[i]=1.0;
END;
j=1;
DO WHILE (j<=d); /* the De Boor formula, refer to Eilers & Marx (1996) */
DO i = 1 TO (n_ext-j-1);
w1 = (x-all_knots[i])/(all_knots[i+j] - all_knots[i]);
w2 = (all_knots[i+j+1]-x)/(all_knots[i+j+1] - all_knots[i+1]);
tmp[i] = w1*tmp[i] +w2*tmp[i+1];
END;
j=j+1;
END;
RETURN(tmp[1:(n_ext-d-1)]);
FINISH my_Bspline;
START my_vec_Bspline(xx, knots, d);
/* evaluate the values of the (num of knots) + d +1 B-spline basis functions at xx */
/* xx is a vector of real numbers*/
/* output a real matrix with dim(xx) rows, and (num of knots) + d +1 columns */
n_row = ncol(xx);
n_col = ncol(knots)+2-d-1;
out = J(n_row, n_col, .);
DO i=1 TO n_row;
out[i, ] = t(my_Bspline(xx[i], knots, d));
END;
RETURN(out);
FINISH my_vec_Bspline;
START GenerateTimeBasis(TimeBasis,Time, InteriorKnots,deg);
* B-Spline basis;
dx = InteriorKnots[1] - Time[><];
EarlyKnots = InteriorKnots[><]-dx*((deg):1);
LateKnots = InteriorKnots[<>]+dx*(1:(deg));
AllKnots = EarlyKnots || InteriorKnots || LateKnots;
CREATE MixTVEMAllBSplineKnots FROM AllKnots;
APPEND FROM AllKnots;
CLOSE MixTVEMAllBSplineKnots;
TimeBasis = my_vec_Bspline(Time`, AllKnots, deg);
FINISH GenerateTimeBasis;
START PrepareRegressionMatrix;
USE MixTVEMData;
READ ALL VAR {&time} INTO Time;
CLOSE MixTVEMData;
USE MixTVEMSettings;
READ ALL VAR {deg MacroError NumCov
NumTCov
UseRoughnessPenalty RoughnessPenalty};
CLOSE MixTVEMSettings;
USE MixTVEMInteriorKnotsMatrix;
READ ALL INTO InteriorKnotsMatrix;
CLOSE MixTVEMInteriorKnotsMatrix;
IF (NumCov > 0) THEN DO;
USE MixTVEMData;
READ ALL VAR{&MixTVEMCov} INTO Cov;
CLOSE MixTVEMData;
Regressors = Cov;
whichBeta = J(NCOL(Cov),1,.);
whichThetaWithinBeta = (1:NCOL(Cov))`;
END;
IF (NumTCov > 0) THEN DO;
USE MixTVEMData;
READ ALL VAR{&MixTVEMTCov} INTO TCov;
CLOSE MixTVEMData;
tcovStdDev = J(NCOL(TCov),1,1);
DO thisTCov = 1 TO NCOL(TCov);
IF NROW(TCov)>1 THEN DO;
TcovStdDev[thisTCov] = SQRT(((TCov[,thisTCov]-TCov[:,thisTCov])[##])/(NROW(TCov[,thisTCov])-1));
END;
IF (ABS(TcovStdDev[thisTCov])<1e-20) THEN DO;
IF tcov[<>,thisTCov]=1 THEN DO;
TcovStdDev[thisTCov] = 1; /* don't rescale intercept term */
END;
END;
InteriorKnots = InteriorKnotsMatrix[LOC(InteriorKnotsMatrix[,thisTCov]^=.), thisTCov]`;
CALL GenerateTimeBasis(TimeBasis,
Time,
InteriorKnots,
deg);
datasetName = COMPRESS(CONCAT("MixTVEMTimeBasis",CHAR(thisTCov)));
commandText = CONCAT("CREATE ",
datasetName,
" FROM TimeBasis;",
" APPEND FROM TimeBasis;",
" CLOSE ",
datasetName,
";");
CALL EXECUTE(commandText);
covariateTimesTimeBasis = TCov[,thisTCov]#TimeBasis;
IF ((NumCov=0)&(thisTCov =1)) THEN DO;
Regressors = covariateTimesTimeBasis;
whichBeta = J(NCOL(TimeBasis),1,thisTCov);
whichThetaWithinBeta = (1:NCOL(TimeBasis))`;
END; ELSE DO;
Regressors = Regressors || covariateTimesTimeBasis;
whichBeta = whichBeta // J(NCOL(TimeBasis),1,thisTCov);
whichThetaWithinBeta = whichThetaWithinBeta // (1:NCOL(TimeBasis))`;
END;
END;
END;
IF (UseRoughnessPenalty>0) THEN DO;
PenaltyMatrix = J(NROW(whichBeta),NROW(whichBeta),0);
IF whichBeta[<>]>0 THEN DO;
DO i = 1 TO whichBeta[<>];
IF (whichBeta[i] >0) THEN DO;
n_theta = NCOL(LOC(whichBeta=i));
PenaltyMatrix[LOC(whichBeta=i),LOC(whichBeta=i)] =
CreatePenaltyMatrix(n_theta);
END;
END;
END;
TVScales = J(nrow(whichBeta),1,1);
DO i = 1 TO whichBeta[<>];
IF tcovStdDev[i]>0 THEN TVScales[LOC(whichBeta=i)]=1/(tcovStdDev[i]+1e-20);
END;
PenaltyMatrix = TVScales#TVScales#PenaltyMatrix;
END;
CREATE MixTVEMRegressors FROM Regressors; APPEND FROM Regressors; CLOSE MixTVEMRegressors;
CREATE MixTVEMWhichBeta FROM whichBeta; APPEND FROM whichBeta; CLOSE MixTVEMWhichBeta;
CREATE MixTVEMWhichThetaWithinBeta FROM whichThetaWithinBeta; APPEND FROM whichThetaWithinBeta; CLOSE MixTVEMWhichThetaWithinBeta;
IF (UseRoughnessPenalty>0) THEN DO;
CREATE MixTVEMPenaltyMatrix FROM PenaltyMatrix; APPEND FROM PenaltyMatrix; CLOSE MixTVEMPenaltyMatrix;
END;
EDIT MixTVEMSettings VAR{MacroError};
MacroError = MacroError;
REPLACE;
CLOSE MixTVEMSettings;
FINISH PrepareRegressionMatrix;
START CreatePenaltyMatrix(n);
/* The R version is
crossprod(diff(diff(diag(as.vector(rep(1,n))))));
see Eilers & Marx (1996) p. 100 */
M = J(n,n,0);
IF n>2 THEN DO;
DO r = 1 TO n;
DO c = 1 TO n;
IF r = c THEN DO;
M[r,c] = 6;
IF ((r=1)|(r=n)) THEN M[r,c] = 1;
IF ((r=2)|(r=n-1)) THEN DO;
IF n>3 THEN M[r,c] = 5; ELSE M[r,c] = 4;
END;
END;
IF (ABS(r-c)=1) THEN DO;
M[r,c] = -4;
IF ((r=1)|(c=1)|(r=n)|(c=n)) THEN M[r,c] = -2;
END;
IF (ABS(r-c)=2) THEN DO;
M[r,c] = 1;
END;
END;
END;
END;
RETURN(M);
FINISH CreatePenaltyMatrix;
START WeightedLogistic(b,w,x,y);
localw = w[LOC(y^=.)];
localx = x[LOC(y^=.),];
localy = y[LOC(y^=.)];
b = J(NCOL(localx),1,0);
MaxAbsDev = 10000000;
CriterionMaxAbsDev = 1e-8;
MaxIter=1000;
iter=0;
DO UNTIL((iter=maxIter) | (maxAbsDev<=criterionMaxAbsDev));
iter = iter + 1;
bOld = b;
expEta = EXP(((localx*b)><20)<>-20);
mu = expEta/(1+expEta);
b = b + SOLVE(localx`*(mu#(1-mu)#localw#localx),
localx`*(localw#(localy-mu)));
maxAbsDev = MAX(ABS(b-bOld));
END;
FINISH WeightedLogistic;
START WeightedLeastSquares(b,w,x,y);
b = SOLVE( x`*(w#x), x`*(w#y) );
FINISH WeightedLeastSquares;
START WeightedRidgeRegression(b,w,x,y,RoughnessPenalty,PenaltyMatrix);
b = SOLVE( x`*(w#x)+RoughnessPenalty*PenaltyMatrix, x`*(w#y) );
FINISH WeightedRidgeRegression;
START WeightedTrace(trace,w,x,y,UseRoughnessPenalty,RoughnessPenalty,PenaltyMatrix);
IF ((UseRoughnessPenalty>0) ) THEN DO;
XTWXinv = INV(x`*(w#x)+RoughnessPenalty*PenaltyMatrix);
END; ELSE DO;
XTWXinv = INV(x`*(w#x));
END;
trace = 0;
DO K = 1 TO NCOL(x);
DO M = 1 TO NCOL(X);
trace = trace + ((XTWXinv)[k,m]*w#x[,k]#x[,m])[+,+];
END;
END;
FINISH;
START DebugAssertEqual(a,b,MacroError);
IF (a^=b) THEN DO;
PRINT("Error in macro");
MacroError = 1;
END;
FINISH DebugAssertEqual;
START CopyToLongForm(longTarget,shortSource,intID);
longTarget = J(NROW(intID),NCOL(shortSource),0);
DO I = 1 TO NROW(shortSource);
longTarget[LOC(intID=i),] = shortSource[i,] @ J(SUM(intID=i),1,1);
END;
FINISH CopyToLongForm;
START InitialRandomEStep;
postProbsBySubject = J(NumSubjects,NumClasses,0);
CALL RANDGEN(postProbsBySubject,"exponential");
postProbsBySubject = (1/postProbsBySubject[,+])#postProbsBySubject;
InitialRun = 1;
FINISH InitialRandomEStep;
START EStep;
/* Get new likelihood contributions and posterior probabilities; */
logProbability = J(numSubjects,numClasses,0);
DO class = 1 TO numClasses;
logProbability[,class] = -(numObsBySubject/2)*
LOG(2*3.1415926535*(sigsq[class]+1e-30)) -
rssBySubjectAndClass[,class]/(2*sigsq[class]+1e-30);
END;
tempMatrix = logProbability;
tempMatrix = tempMatrix + LOG(fittedProb+1e-30);
logLikelihood = (LOG((EXP(tempMatrix))[,+]))[+];
tempMax = tempMatrix[,<>];
tempMatrix = tempMatrix-tempMax;
expTempMatrix = EXP(tempMatrix);
postProbsBySubject = (expTempMatrix+gammaStabilizingConstant/numSubjects) /
(expTempMatrix[,+]+numClasses*gammaStabilizingConstant/numSubjects);
InitialRun = 0;
FINISH EStep;
START MStep;
/* ... for Theta ... */
Theta = J(NCOL(X),numClasses,.);
DO class = 1 TO numClasses;
IF (UseRoughnessPenalty>0) THEN DO;
CALL WeightedRidgeRegression(b,
postProbsByAssessment[,class],
X,
Y,
RoughnessPenalty,
PenaltyMatrix);
Theta[,class] = b;
END; ELSE DO;
CALL WeightedLeastSquares(b,
postProbsByAssessment[,class],
X,
Y);
Theta[,class] = b;
END;
END;
fittedY = X*Theta;
* bestClassThisSubject = postProbsByAssessment[,<:>];
* PRINT bestClassThisSubject;
* bestClassFittedY = fittedY[:,bestClassThisSubject];
sqdResidY = (fittedY - Y@J(1,numClasses,1))##2;
rssBySubjectAndClass = J(numSubjects,numClasses,0);
numObsBySubject = J(numSubjects,1,0);
DO i = 1 TO numSubjects;
rssBySubjectAndClass[i,] = (sqdResidY[LOC(intId=i),])[+,];
numObsBySubject[i] = NCOL(LOC(intId=i));
END;
/* ... for sigma squareds ... */
IF (equalVariance=1) THEN DO;
sigsq = J(1,numClasses,(postProbsBySubject#rssBySubjectAndClass)[+,+]/numTotal);
END; ELSE DO;
sigsq = ((rssBySubjectAndClass#postProbsBySubject)[+,])/
((numObsBySubject#postProbsBySubject)[+,]);
END;
IF ((sigsq[<>]/sigsq[><])>maxVarianceRatio) THEN DO;
sigsq[LOC(sigsq<(sigsq[<>]/maxVarianceRatio))]=sigsq[<>]/maxVarianceRatio;
END;
/* ... and for gammas ... */
USE MixTVEMSBySub; READ ALL INTO S; CLOSE MixTVEMSCov;
SForLogisticRegression = S @ J(numClasses,1,1);
ClassForLogisticRegression = SHAPE((1:numClasses) @ J(numSubjects,1,1),
numClasses*numSubjects);
WeightsForLogisticRegression = SHAPE(PostProbsBySubject,numClasses*numSubjects);
IF (numClasses>1) THEN DO;
NonRefClasses = (1:numClasses)[LOC((1:numClasses)^=refClass)];
END;
gamma = J(NCOL(S),numClasses,0);
IF (NumClasses>1) THEN DO;
expEta = J(numSubjects,numClasses,1);
DO NonRefClassIndex = 1 TO NROW(NonRefClasses);
ThisNonRefClass = NonRefClasses[NonRefClassIndex];
OutcomeForLogisticRegression = 1*(ClassForLogisticRegression=ThisNonRefClass);
IF (NROW(LOC((ClassForLogisticRegression^=ThisNonRefClass)
&(ClassForLogisticRegression^=RefClass)))>0) THEN DO;
OutcomeForLogisticRegression[LOC((ClassForLogisticRegression^=ThisNonRefClass)
&(ClassForLogisticRegression^=RefClass))] = .;
END;
CALL WeightedLogistic(b,
WeightsForLogisticRegression,
SForLogisticRegression,
OutcomeForLogisticRegression);
gamma[,ThisNonRefClass] = b;
expEta[,ThisNonRefClass] = EXP(S*b);
END;
fittedProb = (expEta+gammaStabilizingConstant/numSubjects) /
(expEta[,+]+numClasses*gammaStabilizingConstant/numSubjects);
END; ELSE DO;
fittedProb = J(numSubjects,1,1);
END;
FINISH MStep;
START EMLoop;
%PUT RunningEMLoop;
OldTheta = 1e20;
OldGamma = 1e20;
maxAbsDev = 1e20;
iteration = 0;
Converged = 0;
DO UNTIL ((maxAbsDev<Convergence)|(iteration > MaxIterationsToUse));
iteration = iteration + 1;
postProbsByAssessment = J(NumTotal,NumClasses,0);
CALL CopyToLongForm(postProbsByAssessment,postProbsBySubject,intID);
CALL MStep;
CALL EStep;
maxAbsDev = MAX( (ABS(gamma-oldGamma))[<>,<>], (ABS(theta-oldTheta))[<>,<>]);
oldGamma = Gamma;
oldTheta = Theta;
END;
IF ((maxAbsDev>Convergence)&(runSilent=0)) THEN DO;
PRINT "Warning - EM Algorithm Failed to converge";
MacroError = 1;
END; ELSE DO;
Converged = 1;
END;
ClassPrevalences = fittedProb[+,]/numSubjects;
FINISH EMLoop;
START FitTheModel;
CALL RANDSEED(BestSeed,1);
CALL InitialRandomEStep;
MaxIterationsToUse = MaxIterations;