The GENMOD Procedure

REPEATED Statement

REPEATED SUBJECT=subject-effect </ options> ;

The REPEATED statement specifies the covariance structure of multivariate responses for GEE model fitting in the GENMOD procedure. In addition, the REPEATED statement controls the iterative fitting algorithm used in GEEs and specifies optional output. Other GENMOD procedure statements, such as the MODEL and CLASS statements, are used in the same way as they are for ordinary generalized linear models to specify the regression model for the mean of the responses.

Table 40.8 summarizes the options available in the REPEATED statement.

Table 40.8: REPEATED Statement Options

Option	Description
ALPHAINIT=	Specifies initial values for log odds ratio regression parameters
CONVERGE=	Specifies the convergence criterion for GEE parameter estimation
CORRB	Displays the estimated correlation matrix
CORRW	Displays the estimated working correlation matrix
COVB	Displays the estimated covariance matrix
ECORRB	Displays the estimated empirical correlation matrix
ECOVB	Displays the estimated empirical covariance matrix
INITIAL=	Specifies initial values of the regression parameters estimation
INTERCEPT=	Specifies either an initial or a fixed value of the intercept
LOGOR=	Specifies the regression structure of the log odds ratio
MAXITER=	Specifies the maximum number of iterations
MCORRB	Displays the estimated model-based correlation matrix
MCOVB	Displays the estimated model-based covariance matrix
MODELSE	Displays an analysis of parameter estimates table
PRINTMLE	Displays an analysis of maximum likelihood parameter estimates table
RUPDATE=	Specifies the number of iterations between updates of the working correlation matrix
SORTED	Groups by subject and sorts within subject
SUBCLUSTER=	Specifies a variable defining subclusters
SUBJECT=	Identifies a different subject, or cluster
TYPE=	Specifies the working correlation matrix structure
V6CORR	Uses the SAS ‘Version 6’ method of computing normalized Pearson chi-square
WITHIN=	Specifies the order of measurements within subjects
YPAIR=	Specifies the pairs of responses
ZDATA=	Specifies the full $\mb {z}$ matrix
ZROW=	Specifies the rows of the $\mb {z}$ matrix

SUBJECT=subject-effect

identifies subjects in the input data set. The subject-effect can be a single variable, an interaction effect, a nested effect, or a combination. Each distinct value, or level, of the effect identifies a different subject, or cluster. Responses from different subjects are assumed to be statistically independent, and responses within subjects are assumed to be correlated. A subject-effect must be specified, and variables used in defining the subject-effect must be listed in the CLASS statement. The input data set does not need to be sorted by subject (see the SORTED option).

The options control how the model is fit and what output is produced. You can specify the following options after a slash (/).

ALPHAINIT=numbers

specifies initial values for log odds ratio regression parameters if the LOGOR= option is specified for binary data. If this option is not specified, an initial value of 0.01 is used for all the parameters.

CONVERGE=number

specifies the convergence criterion for GEE parameter estimation. If the maximum absolute difference between regression parameter estimates is less than the value of number on two successive iterations, convergence is declared. If the absolute value of a regression parameter estimate is greater than 0.08, then the absolute difference normalized by the regression parameter value is used instead of the absolute difference. The default value of number is 0.0001.

CORRW

displays the estimated working correlation matrix. If you specify an exchangeable working correlation structure with the CORR=EXCH option, the CORRW option is not needed to view the estimated correlation, since a table is printed by default that contains the single estimated correlation.

CORRB

displays the estimated regression parameter correlation matrix. Both model-based and empirical correlations are displayed.

COVB

displays the estimated regression parameter covariance matrix. Both model-based and empirical covariances are displayed.

ECORRB

displays the estimated regression parameter empirical correlation matrix.

ECOVB

displays the estimated regression parameter empirical covariance matrix.

INTERCEPT=number

specifies either an initial or a fixed value of the intercept regression parameter in the GEE model. If you specify the NOINT option in the MODEL statement, then the intercept is fixed at the value of number.

INITIAL=numbers

specifies initial values of the regression parameters estimation, other than the intercept parameter, for GEE estimation. If this option is not specified, the estimated regression parameters assuming independence for all responses are used for the initial values.

LOGOR=log-odds-ratio-structure-keyword

specifies the regression structure of the log odds ratio used to model the association of the responses from subjects for binary data. The response syntax must be of the single variable type, the distribution must be binomial, and the data must be binary. Table 40.9 displays the log odds ratio structure keywords and the corresponding log odds ratio regression structures. See the section Alternating Logistic Regressions for definitions of the log odds ratio types and examples of specifying log odds ratio models. You should specify either the LOGOR= or the TYPE= option, but not both.

Table 40.9: Log Odds Ratio Regression Structures

Keyword	Log Odds Ratio Regression Structure
EXCH	Exchangeable
FULLCLUST	Fully parameterized clusters
LOGORVAR(variable)	Indicator variable for specifying block effects
NESTK	k-nested
NEST1	1-nested
ZFULL	Fully specified $\mb {z}$ matrix specified in ZDATA= data set
ZREP	Single cluster specification for replicated $\mb {z}$ matrix specified
	in ZDATA= data set
ZREP(matrix)	Single cluster specification for replicated $\mb {z}$ matrix

MAXITER=number MAXIT=number

specifies the maximum number of iterations allowed in the iterative GEE estimation process. The default number is 50.

MCORRB

displays the estimated regression parameter model-based correlation matrix.

MCOVB

displays the estimated regression parameter model-based covariance matrix.

MODELSE

displays an analysis of parameter estimates table that uses model-based standard errors for inference. By default, an “Analysis of Parameter Estimates” table based on empirical standard errors is displayed.

PRINTMLE

displays an analysis of maximum likelihood parameter estimates table. The maximum likelihood estimates are not displayed unless this option is specified.

RUPDATE=number

specifies the number of iterations between updates of the working correlation matrix. For example, RUPDATE=5 specifies that the working correlation is updated once for every five regression parameter updates. The default value of number is 1; that is, the working correlation is updated every time the regression parameters are updated.

SORTED

specifies that the input data are grouped by subject and sorted within subject. If this option is not specified, then the procedure internally sorts by subject-effect and within subject-effect, if a within subject-effect is specified.

SUBCLUSTER=variable SUBCLUST=variable

specifies a variable defining subclusters for the 1-nested or k-nested log odds ratio association modeling structures. This variable must be listed in the CLASS statement.

TYPE=correlation-structure keyword CORR=correlation-structure keyword

specifies the structure of the working correlation matrix used to model the correlation of the responses from subjects. Table 40.10 displays the correlation structure keywords and the corresponding correlation structures. The default working correlation type is the independent (CORR=IND). See the section Details: GENMOD Procedure for definitions of the correlation matrix types. You should specify LOGOR= or TYPE= but not both.

Table 40.10: Correlation Structure Types

Keyword	Correlation Matrix Type
AR
AR(1)	Autoregressive(1)
EXCH
CS	Exchangeable
IND	Independent
MDEP(number)	m-dependent with m=number
UNSTR
UN	Unstructured
USER
FIXED (matrix)	Fixed, user-specified correlation matrix

For example, you can specify a fixed $4 \times 4$ correlation matrix with the following option:

type=user( 1.0  0.9  0.8  0.6
           0.9  1.0  0.9  0.8
           0.8  0.9  1.0  0.9
           0.6  0.8  0.9  1.0 )

V6CORR

specifies that the SAS ‘Version 6’ method of computing the normalized Pearson chi-square be used for working correlation estimation and for model-based covariance matrix scale factor.

WITHINSUBJECT | WITHIN=within subject-effect

defines an effect specifying the order of measurements within subjects. Each distinct level of the within subject-effect defines a different response from the same subject. If the data are in proper order within each subject, you do not need to specify this option.

If some measurements do not appear in the data for some subjects, this option properly orders the existing measurements and treats the omitted measurements as missing values. If the WITHINSUBJECT= option is not used in this situation, measurements might be improperly ordered and missing values assumed for the last measurements in a cluster.

Variables used in defining the within subject-effect must be listed in the CLASS statement.

YPAIR=variable-list

specifies the variables in the ZDATA= data set corresponding to pairs of responses for log odds ratio association modeling.

ZDATA=SAS-data-set

specifies a SAS data set containing either the full $\mb {z}$ matrix for log odds ratio association modeling or the $\mb {z}$ matrix for a single complete cluster to be replicated for all clusters.

ZROW=variable-list

specifies the variables in the ZDATA= data set corresponding to rows of the $\mb {z}$ matrix for log odds ratio association modeling.