Re: Output from POWER UNIVARIATE LINEAR

Posted by Bruce Weaver on
URL: http://spssx-discussion.165.s1.nabble.com/Output-from-POWER-UNIVARIATE-LINEAR-tp5740814p5740816.html

Thanks for jumping in, Richard.  

Actually, I like the TEST_PREDICTORS keyword in the syntax just fine.  My main complaint is that the OUTPUT should say Full vs Tested under Predictors rather than Full vs Nested.  

Let's go back to the example I was attempting.  Here it is:

Consider a test of the significance of two covariates in a multiple linear regression adjusting for three other covariates. We will call the two covariates the tested covariates and the three others control covariates. The reduced model with the control covariates has an R2 of 0.1, and the full model with all five covariates has an R2 of 0.2. We want to compute the required sample size for the two-sided R2 test to achieve 80% power with a 5% significance level—power rsquared defaults.  (Source:  https://www.stata.com/features/overview/power-analysis-for-linear-regression-models/)

The Stata output, which gives the same sample size estimate as SPSS, shows the following:

power rsquared 0.1 0.2, ntested(2) ncontrol(3)

Estimated sample size for multiple linear regression
F test for R2 testing subset of coefficients
Ho: R2_F = R2_R  versus  Ha: R2_F != R2_R

Study parameters:

        alpha =    0.0500
        power =    0.8000
        delta =    0.1250
         R2_R =    0.1000  <<< Rsq for the reduced model with 3 variables
         R2_F =    0.2000  <<< Rsq for the full model with all 5 variables
      R2_diff =    0.1000
     ncontrol =         3    <<< number of variables in the reduced model
      ntested =         2   <<< number of variables added in the 2nd block

Estimated sample size:

            N =        81   <<< This matches the result I got using SPSS


Here is the SPSS output again (so you don't have to look at another post):



First, notice that in the Test Assumptions columns, Rsq = .2 for the Full model and Rsq = .1 for the "Nested" model.  This suggests that SPSS is using "nested" model to mean "reduced" model.  

Now look at the Predictors columns.  The full model is correctly shown to have 5 predictors.  But the "nested" (aka., reduced) model is incorrectly shown to have 2 predictors.  The reduced model in this example has 3 predictors, not 2.  Two predictors are added to the reduced model to reach 5 predictors in the full model.  And the test is the F-test on the change in Rsq when adding those 2 variables.  So NTESTED = 2, as shown in the command syntax:

POWER UNIVARIATE LINEAR
  /PARAMETERS MODEL=FIXED SIGNIFICANCE=0.05 POWER=0.8
   TOTAL_PREDICTORS=5 TEST_PREDICTORS=2
    FULL_MODEL=0.2 NESTED_MODEL=0.1 INTERCEPT =TRUE.

Finally, if I redo the problem with k=2 variables in block 1 (the reduced model) and k=5 variables in the full model (i.e., with ntested=3), I get n = 92 as the estimated sample size.  (Both SPSS and Stata give that same result.)  

I hope this clarifies the nature of my complaint!  ;-)  

Cheers,
Bruce

Richard M wrote

A response from one of our statistical team:

Based on my understanding, the customer dislikes the keyword TEST_PREDICTORS in syntax, and considers it confusing.


I am aware that NESTED_PREDICTORS could be a better keyword in this case. In our UI, it should be clear.



However, the syntax pastes the same keyword for either of the following two cases:



I think this is consistent with the online help which says:

TEST_PREDICTORS = integer
A required keyword that specifies the number of either the test predictors or the predictors in the nested model (not including the intercept if applicable). When PARTIAL_CORR is specified, the value must be a single integer ∈[1,p], where p is the value specified for TOTAL_PREDICTORS. When FULL_MODEL and NESTED_MODEL are specified, the value must be a single integer ∈[1,p), where p is the value specified for TOTAL_PREDICTORS.