Shared Concepts and Topics

specifies how denominator degrees of freedom are determined when p-values and confidence limits are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the ADJDFE= option, or when you specify ADJDFE=SOURCE, the denominator degrees of freedom for multiplicity-adjusted results are the denominator degrees of freedom for the final effect that is listed in the ESTIMATE statement from the "Type III" table.

The ADJDFE=ROW setting is useful if you want multiplicity adjustments to take into account that denominator degrees of freedom are not constant across estimates. For example, this can be the case when the denominator degrees of freedom are computed by the Satterthwaite method or according to Kenward and Roger (1997).

The ADJDFE= option has an effect only in mixed models that use these degree-of-freedom methods. It is not supported by the procedures that perform chi-square-based inference (LOGISTIC, PHREG, and SURVEYLOGISTIC).

requests a multiple comparison adjustment for the p-values and confidence limits for the estimates. The adjusted quantities are produced in addition to the unadjusted quantities. Adjusted confidence limits are produced if the CL or ALPHA= option is in effect. For a description of the adjustments, see Chapter 53, The GLM Procedure, and Chapter 86, The MULTTEST Procedure, and the documentation for the ADJUST= option in the LSMEANS statement.

If the STEPDOWN option is in effect, the p-values are further adjusted in a step-down fashion.

requests that a t type confidence interval be constructed with confidence level 1 – number. The value of number must be between 0 and 1; the default is 0.05. If the "Estimates" table shows infinite degrees of freedom, then the confidence interval is a z type interval.

specifies how to construct estimates and multiplicity corrections for models that contain multinomial response data (ordinal or nominal). This option is also important for constructing sets of estimable functions for F or chi-square tests with the JOINT option.

The category-options are used to indicate how response variable levels are treated in constructing the estimable functions. Possible values for the category-options are the following:

Consider the following ESTIMATE statements in the LOGISTIC procedure for an ordinal model that has response categories 'vg', 'g', 'm', 'b', and 'vb'. Because there are five response categories, there are four nonredundant categories for the cumulative link model.

proc logistic data=icecream;
   class brand / param=glm;
   model taste(order=data) = brand / link=logit;
   freq count;

   estimate brand 1 -1,
            intercept 1 brand  0 1 / category='m','vg';

   estimate intercept 1 brand 1    / category=joint
                                     adjust=simulate(seed=1);

   estimate brand 1 -1,
            brand 1 1 -2           / category=separate
                                     adjust=bon;
run;

The first ESTIMATE statement requests a two-row estimable function: the first row compares the first two brands, and the second row estimates the second brand. The result is produced for two of the four nonredundant response categories. The second ESTIMATE statement produces estimates for the first brand in all four nonredundant categories and displays them in a single table. The multiplicity adjustment with p-value computation by simulation treats the four estimable functions as a unit for familywise Type I error protection. The third ESTIMATE statement computes a two-row estimable function: the first row again compares the first two brands, and the second row compares the average of the first two brands to the third. The result is displayed in separate tables, one for each nonredundant category. The Bonferroni adjustment in this statement applies to a family of two tests that correspond to the two-row estimable function. Four Bonferroni adjustments for sets of size two are performed.

The CATEGORY= option is supported only by the procedures that support generalized linear modeling (GEE, LOGISTIC, and SURVEYLOGISTIC) and by PROC PLM when it is used to perform statistical analyses on item stores created by these procedures.

requests that chi-square tests be performed in addition to F tests, when you request an F test with the JOINT option. This option has no effect in procedures that produce chi-square statistics by default.

requests that t type confidence limits be constructed. If the procedure shows the degrees of freedom in the "Estimates" table as infinite, then the confidence limits are z intervals. The confidence level is 0.95 by default, and you can change the confidence level with the ALPHA= option. The confidence intervals are adjusted for multiplicity when you specify the ADJUST= option. However, if a step-down p-value adjustment is requested with the STEPDOWN option, only the p-values are adjusted for multiplicity.

displays the estimated correlation matrix of the linear combination of the parameter estimates.

displays the estimated covariance matrix of the linear combination of the parameter estimates.

specifies the degrees of freedom for the t test and confidence limits. This option is not supported by the procedures that perform chi-square-based inference (LOGISTIC, PHREG, and SUVEYLOGISTIC).

specifies a list of values by which to divide the coefficients so that fractional coefficients can be entered as integer numerators. If you do not specify value-list, a default value of 1.0 is assumed. Missing values in the value-list are converted to 1.0.

If the number of elements in value-list exceeds the number of rows of the estimate, the extra values are ignored. If the number of elements in value-list is less than the number of rows of the estimate, the last value in value-list is copied forward.

If you specify a row-specific divisor as part of the specification of the estimate row, this value multiplies the corresponding divisor that is implied by the value-list. For example, the following statement divides the coefficients in the first row by 8, and the coefficients in the third and fourth row by 3:

estimate 'One vs. two'   A 2 -2  (divisor=2),
         'One vs. three' A 1  0 -1         ,
         'One vs. four'  A 3  0  0 -3      ,
         'One vs. five'  A 1  0  0  0  -1  / divisor=4,.,3;

Coefficients in the second row are not altered.

requests that the matrix coefficients be displayed.

requests exponentiation of the estimate. When you model data with the logit, cumulative logit, or generalized logit link functions, and the estimate represents a log odds ratio or log cumulative odds ratio, the EXP option produces an odds ratio. In proportional hazards model, this option produces estimates of hazard ratios. If you specify the CL or ALPHA= option, the (adjusted) confidence bounds are also exponentiated.

The EXP option is supported only by PROC PHREG, PROC SURVEYPHREG, the procedures that support generalized linear modeling (GEE, LOGISTIC and SURVEYLOGISTIC), and by PROC PLM when it is used to perform statistical analyses on item stores created by these procedures.

requests that the estimate and its standard error also be reported on the scale of the mean (the inverse linked scale). The computation of the inverse linked estimate depends on the estimation mode. For example, if the analysis is based on a posterior sample when a BAYES statement is present, the inversely linked estimate is the average of the inversely linked values across the sample of posterior parameter estimates. If the analysis is not based on a sample of parameter estimates, the procedure computes the value on the mean scale by applying the inverse link to the estimate. The interpretation of this quantity depends on the effect values specified in your ESTIMATE statement and on the link function. For example, in a model for binary data with logit link the following statements compute

where and are the fixed-effects solutions that are associated with the first two levels of the classification effect A:

class A;
model y = A / dist=binary link=logit;
estimate 'A one vs. two' A 1 -1 / ilink;

This quantity is not the difference of the probabilities that are associated with the two levels,

The standard error of the inversely linked estimate is based on the delta method. If you also specify the CL option, the procedure computes confidence limits for the estimate on the mean scale. In multinomial models for nominal data, the limits are obtained by the delta method. In other models they are obtained from the inverse link transformation of the confidence limits for the estimate. The ILINK option is specific to an ESTIMATE statement.

The ILINK option is supported only by the procedures that support generalized linear modeling (GEE, LOGISTIC and SURVEYLOGISTIC) and by PROC PLM when it is used to perform statistical analyses on item stores created by these procedures.

requests that a joint F or chi-square test be produced for the rows of the estimate. The JOINT option in the ESTIMATE statement essentially replaces the CONTRAST statement. For multinomial response models, a joint test is constructed for each response function.

When the LOWERTAILED or the UPPERTAILED options are in effect, or if the BOUNDS option described below is in effect, the JOINT option produces the chi-bar-square statistic according to Silvapulle and Sen (2004). This statistic uses a simulation-based approach to compute p-values in situations where the alternative hypotheses of the estimable functions are not simple two-sided hypotheses. See the section Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square Statistic for more information about this test statistic.

You can specify the following joint-test-options in parentheses:

requests that the p-value for the t test be based only on values that are less than the test statistic. A two-tailed test is the default. A lower-tailed confidence limit is also produced if you specify the CL or ALPHA= option.

Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted p-values are the same as the corresponding two-sided statistics, because this adjustment is based on only the right tail of the F distribution.

If you request a joint test with the JOINT option, then a one-sided left-tailed order restriction is applied to all estimable functions, and the corresponding chi-bar-square statistic of Silvapulle and Sen (2004) is computed in addition to the two-sided, standard, F or chi-square statistic. See the JOINT option for how to control the computation of the simulation-based chi-bar-square statistic.

suppresses the automatic fill-in of coefficients of higher-order effects.

produces ODS statistical graphics of the distribution of estimable functions if the procedure performs the analysis in a sampling-based mode. For example, this is the case when procedures support a BAYES statement and perform a Bayesian analysis. The estimable functions are then computed for each of the posterior parameter estimates, and the "Estimates" table reports simple descriptive statistics for the evaluated functions. The PLOTS= option enables you in this situation to visualize the distribution of the estimable function. The following plot-options are available:

specifies the seed for the sampling-based components of the computations for the ESTIMATE statement (for example, chi-bar-square statistics and simulated p-values). The value of number must be an integer. The seed is used to start the pseudo-random number generator for the simulation. If you do not specify a seed, or if you specify a value less than or equal to zero, the seed is generated from reading the time of day from the computer clock. There could be multiple ESTIMATE statements with SEED= specifications and there could be other statements that can supply a random number seed. Since the procedure has only one random number stream, the initial seed is shown in the SAS log.

tunes the estimability checking. If is a vector, define ABS() to be the largest absolute value of the elements of . If ABS() is greater than c*number for any row of in the contrast, then is declared nonestimable. Here, is the Hermite form matrix , and c is ABS(), except when it equals 0, and then c is 1. The value for number must be between 0 and 1; the default is 1E–4.

requests that multiplicity adjustments for the p-values of estimates be further adjusted in a step-down fashion. Step-down methods increase the power of multiple testing procedures by taking advantage of the fact that a p-value is never declared significant unless all smaller p-values are also declared significant. The STEPDOWN adjustment combined with ADJUST=BON corresponds to the methods of Holm (1979) and "Method 2" of Shaffer (1986); this is the default. Using step-down-adjusted p-values combined with ADJUST=SIMULATE corresponds to the method of Westfall (1997).

If the ESTIMATE statement is applied with a STEPDOWN option in a mixed model where the degrees-of-freedom method is that of Kenward and Roger (1997) or of Satterthwaite, then step-down-adjusted p-values are produced only if the ADJDFE=ROW option is in effect.

Also, the STEPDOWN option affects only p-values, not confidence limits. For ADJUST=SIMULATE, the generalized least squares hybrid approach of Westfall (1997) is used to increase Monte Carlo accuracy. You can specify the following step-down-options in parentheses after the STEPDOWN option:

specifies the value under the null hypothesis for testing the estimable functions in the ESTIMATE statement. The rules for specifying the value-list are very similar to those for specifying the divisor list in the DIVISOR= option. If no TESTVALUE= is specified, all tests are performed as . Missing values in the value-list also are translated to zeros. If you specify fewer values than rows in the ESTIMATE statement, the last value in value-list is carried forward.

The TESTVALUE= option affects only p-values from individual, joint, and multiplicity-adjusted tests. It does not affect confidence intervals.

The TESTVALUE option is not available for the multinomial distribution, and the values are ignored when you perform a sampling-based (Bayesian) analysis.

requests that the p-value for the t test be based only on values that are greater than the test statistic. A two-tailed test is the default. An upper-tailed confidence limit is also produced if you specify the CL or ALPHA= option.

Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted p-values are the same as the corresponding two-sided statistics, because this adjustment is based on only the right tail of the F distribution.

If you request a joint test with the JOINT option, then a one-sided right-tailed order restriction is applied to all estimable functions, and the corresponding chi-bar-square statistic of Silvapulle and Sen (2004) is computed in addition to the two-sided, standard, F or chi-square statistic. See the JOINT option for how to control the computation of the simulation-based chi-bar-square statistic.