The MIANALYZE Procedure

Testing Linear Hypotheses about the Parameters

Linear hypotheses for parameters $\bbeta $ are expressed in matrix form as

\[ H_0: \mb{L} \bbeta = \mb{c} \]

where $\mb{L}$ is a matrix of coefficients for the linear hypotheses and $\mb{c}$ is a vector of constants.

Suppose that $\hat{\mb{Q}_ i}$ and $\hat{\mb{U}_ i}$ are the point and covariance matrix estimates, respectively, for a p-dimensional parameter $\mb{Q}$ from the $i\mr{th}$ imputed data set, i=1, 2, …, m. Then for a given matrix $\mb{L}$, the point and covariance matrix estimates for the linear functions $\mb{L} \mb{Q}$ in the $i\mr{th}$ imputed data set are, respectively,

\[ \mb{L} \hat{\mb{Q}_ i} \]
\[ \mb{L} \hat{\mb{U}_ i} \bL ’ \]

The inferences described in the section Combining Inferences from Imputed Data Sets and the section Multivariate Inferences are applied to these linear estimates for testing the null hypothesis $H_0: \mb{L} \bbeta = \mb{c}$.

For each TEST statement, the "Test Specification" table displays the $\mb{L}$ matrix and the $\mb{c}$ vector, the "Variance Information" table displays the between-imputation, within-imputation, and total variances for combining complete-data inferences, and the "Parameter Estimates" table displays a combined estimate and standard error for each linear component.

With the WCOV and BCOV options in the TEST statement, the procedure displays the within-imputation and between-imputation covariance matrices, respectively.

With the TCOV option, the procedure displays the total covariance matrix derived under the assumption that the population between-imputation and within-imputation covariance matrices are proportional to each other.

With the MULT option in the TEST statement, the "Multivariate Inference" table displays an F test for the null hypothesis $\mb{L} \bbeta = \mb{c}$ of the linear components.