I may have found an answer to this question. See answer #3 to FAQ on the following website:

http://homes.ori.org/~keiths/Files/Methods/SAS-FAQ.html

Here is what it says:

"Why do the "Solution for Fixed Effects" and the "Tests of Fixed Effects" sometimes differ?

The F-tests are by default Type III tests, so that if there is an F-test for a main effect involved in an interaction, it is an approximate test for the main effect valid only if the interaction is zero (Murray, 1998, p. 293, note 23). If you look at the t-test in the solution table in the same analysis, the t-test for that same main effect is a test for the simple main effect of that variable at the zero level of the other term involved in the interaction. In other words, the t-tests in the solution table are always interpretable just as any test of a regression coefficient would be from a linear regression analysis, but the F-tests aren't.

Consider male (1=male, 0=female) and cond (condition; 1=intervention, 0=control). If we have an interaction model that includes male, cond and male × cond, the F-test for male is an approximate test of whether males are different from females in general, and is valid only if the interaction effect is zero. In the same analysis, the t-test for male in the solution table is a test of whether males are different from females when we restrict ourselves to students in the control condition. So the t-test and F-test are testing different null hypotheses in that circumstance and their p-values may be different, especially if the interaction effect is meaningful. In a purely main effects model, the t-test and F-test are testing the same null hypothesis and their p-values will be identical. (Answer by David Murray, 04-28-00 e-mail, edited.)

On Murray's (1998) note 23 on page 293, he comments that some controversy lies around Type III F-tests and that people have often misinterpreted them. In an analysis of condition and time, the F-test for condition tests the null hypothesis that condition does not vary at an average level of time. The Type III F-test of time tests for a time effect at the average level of condition. With an interaction, Type III F-tests reduce the denominator degrees of freedom and inflate the standard errors of tests of main effects for the included interaction.

For more information, please read an e-mail exchange on the s-news distribution list about Type III F-tests. "

I do not know is this realy your problem. But , If you run an analysis including only the main effects, you will have type III sum of squares, with corresponding p-values. Which must necessarily be different from a model where the interaction term is present, the reason is simply because if the interaction is significant, it will significantly reduce the sum of squares for the error, and for obligation, the p-values have to change. Only if the sum of squares for the interaction it is zero, you would chance of no change in the inference, but still you have the problem of the loss of degrees of freedom to estimate the experimental error, and their consequences on the inference on the main effects.

I hope this helps.

I do want to add this comment.

If you're referring to the solution of mixed model equations. You have another situation under consideration, you must consider that if the restriction imposed is that the constant last zero for each effect, the solution is not unique, and usually does not make sense even to print it. We know that the difference between the constants is the same regardless of the restriction. But these constants whhen we assume that the last constant of each effect is cero, they have no sense, for interpretation in practice, they depend , for example on the order on which the levels of each variable are classified.

Rafael, thank you very much for your comment.

What I don't understand is discrepancy in p-values in these two tables. Between these 2 tables, I know "Type 3 Tests of Fixed Effects" is the one I should first consider, but the discrepancy makes me feel that "Solution for Fixed Effects" is not reliable.

if I drop out the interaction term, p-value for gp will be the same (p=0.4084), which is what I expect. So is it true that when interaction term is included, we should not see the result from "Solution for Fixed Effects"? Thank you again

proc mixed data=result covtest noclprint; class gp sub time;

model Y = gp time / solution ;

lsmeans gp / pdiff cl;

repeated time / subject=sub type=un;

run;

Solution for Fixed Effects

Standard

Effect gp time Estimate Error DF t Value Pr > |t|

Intercept 3.8166 1.1329 8 3.37 (0.0098)

gp 0 1.1667 1.3373 8 0.87 (0.4084)

gp 1 0 . . . .

time 1 7E-16 0.7149 8 0.00 (1.0000)

time 2 -0.2000 0.4422 8 -0.45 (0.6631)

time 3 0 . . . .

Type 3 Tests of Fixed Effects

Num Den

Effect DF DF F Value Pr > F

gp 1 8 0.76 (0.4084)

time 2 8 3.23 (0.0935)

I may have found an answer to this question. See answer #3 to FAQ on the following website:

http://homes.ori.org/~keiths/Files/Methods/SAS-FAQ.html

Here is what it says:

"Why do the "Solution for Fixed Effects" and the "Tests of Fixed Effects" sometimes differ?

The F-tests are by default Type III tests, so that if there is an F-test for a main effect involved in an interaction, it is an approximate test for the main effect valid only if the interaction is zero (Murray, 1998, p. 293, note 23). If you look at the t-test in the solution table in the same analysis, the t-test for that same main effect is a test for the simple main effect of that variable at the zero level of the other term involved in the interaction. In other words, the t-tests in the solution table are always interpretable just as any test of a regression coefficient would be from a linear regression analysis, but the F-tests aren't.

Consider male (1=male, 0=female) and cond (condition; 1=intervention, 0=control). If we have an interaction model that includes male, cond and male × cond, the F-test for male is an approximate test of whether males are different from females in general, and is valid only if the interaction effect is zero. In the same analysis, the t-test for male in the solution table is a test of whether males are different from females when we restrict ourselves to students in the control condition. So the t-test and F-test are testing different null hypotheses in that circumstance and their p-values may be different, especially if the interaction effect is meaningful. In a purely main effects model, the t-test and F-test are testing the same null hypothesis and their p-values will be identical. (Answer by David Murray, 04-28-00 e-mail, edited.)

On Murray's (1998) note 23 on page 293, he comments that some controversy lies around Type III F-tests and that people have often misinterpreted them. In an analysis of condition and time, the F-test for condition tests the null hypothesis that condition does not vary at an average level of time. The Type III F-test of time tests for a time effect at the average level of condition. With an interaction, Type III F-tests reduce the denominator degrees of freedom and inflate the standard errors of tests of main effects for the included interaction.

For more information, please read an e-mail exchange on the s-news distribution list about Type III F-tests. "

 Daniel, thank you very much for your explanation, which is very useful.