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st: Regarding ANOVA models


From   "Ali Karim" <mehryar@hotmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Regarding ANOVA models
Date   Mon, 03 Feb 2003 23:07:48 +0000

Dear list readers,
I have different results based on model specification that intuitively looks same to me. I have repeated measures, subjects are nested in sex and interviewed in four rounds. My structural equation is:
Y(ijk) = M + round(i) + sex(j) + sub(k|j) + round*sex(ij) + round*sub(ij|k) + e
My data:
. table sex round,c(mean close n close)
--------------------------------------------------
responden | round
t sex | 0 1 2 3
----------+---------------------------------------

female | .6976744 .744186 .744186 .6976744
| 43 43 43 43
|
male | .4883721 .5813953 .6627907 .7093023
| 86 86 86 86
--------------------------------------------------
I write the following syntax (without correction for repeated measures) to get the SS & MS.
. anova close sex round round*sex formno|sex round*formno|sex

Number of obs = 516 R-squared = 1.0000
Root MSE = 0.00 Adj R-squared =
Source | Partial SS df MS F Prob > F
-----------------+----------------------------------------------------
Model | 117.806202 515 .228749906
|
sex | 1.39922481 1 1.39922481
round | .946258154 3 .315419385
round*sex | .810077519 3 .27002584
formno|sex | 89.4069767 127 .703991943
round*formno|sex | 24.4767442 381 .064243423
|
Residual | 0.00 0
-----------------+----------------------------------------------------
Total | 117.806202 515 .228749906

Alternatively I drop the term round*formno|sex from the model to let it show up as residuals. (I use this because Stata estimates the model without the round*formno|sex term much faster)
. anova close sex round round*sex formno|sex

Number of obs = 516 R-squared = 0.7922
Root MSE = .253463 Adj R-squared = 0.7192

Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 93.3294574 134 .696488488 10.84 0.0000
|
sex | 1.39922481 1 1.39922481 21.78 0.0000
round | .934108527 3 .311369509 4.85 0.0025
round*sex | .810077519 3 .27002584 4.20 0.0061
formno|sex | 89.4069767 127 .703991943 10.96 0.0000
|
Residual | 24.4767442 381 .064243423
-----------+----------------------------------------------------
Total | 117.806202 515 .228749906

My question is why should the SS for round effect be different between the two models?



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