The GEE Procedure (Experimental)

REPEATED Statement

REPEATED SUBJECT=subject-effect </ options>;

The REPEATED statement specifies the correlation structure of the responses for GEE model fitting. In addition, the REPEATED statement controls the iterative fitting algorithm and specifies optional output.

Table 42.6 summarizes the options available in the REPEATED statement.

Table 42.6: REPEATED Statement Options

Option	Description
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 an initial value of the intercept
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 a parameter estimates table with the model-based standard errors
SUBJECT=	Identifies a different subject (cluster)
TYPE=	Specifies the working correlation matrix structure
WITHIN=	Specifies the order of measurements within subjects

You must specify the SUBJECT= option:

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 (level) of the effect identifies a different subject (cluster). Responses from different subjects are assumed to be statistically independent, and responses within subjects are assumed to be correlated. You must specify a subject-effect, and you must list variables that are used in defining the subject-effect in the CLASS statement.

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

CONVERGE=number

specifies the convergence criterion for GEE parameter estimation. If the maximum absolute difference between regression parameter estimates is less than 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.

CORRB

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

CORRW

displays the estimated working correlation matrix. If you specify TYPE=EXCH for the exchangeable working correlation structure, then the CORRW option is not needed to view the estimated correlation, because a table that contains the single estimated correlation is printed by default.

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.

INITIAL=numbers

specifies initial values of the regression parameters estimation, other than the intercept parameter, for GEE estimation. If you do not specify this option, then the estimated regression parameters (assuming independence for all responses) are used for the initial values.

INTERCEPT=number

specifies an initial value of the intercept regression parameter in the GEE model.

MAXITER=number MAXIT=number

specifies the maximum number of iterations allowed in the iterative GEE estimation process. By default, MAXITER=50.

MCORRB

displays the estimated regression parameter model-based correlation matrix.

MCOVB

displays the estimated regression parameter model-based covariance matrix.

MODELSE

displays a parameter estimates table that uses model-based standard errors for inference. By default, a "Parameter Estimates" table that is based on empirical standard errors is displayed.

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

specifies the structure of the working correlation matrix that is used to model the correlation of the responses from subjects. You can specify the values that are shown in Table 42.7 (for definitions of the correlation matrix types, see Table 42.8 in the section Details: GEE Procedure):

Table 42.7: Correlation Structure Types

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

By default, TYPE=IND.

For example, the following option specifies a fixed $4 \times 4$ correlation matrix:

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 )

WITHINSUBJECT=within-subject-effect WITHIN=within-subject-effect

defines an effect that specifies 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 you do not specify the WITHIN= option for the standard GEE method, missing values are assumed to be the last values and are not used; the remaining observations are then ordered in the sequence in which they are provided in the input data set. If you do not specify the WITHIN= option for the weighted GEE method, the observations are assumed to be ordered in the sequence in which they are provided in the input data set.

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