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st: repeated measures ANOVA with missing observations

From   "David L. Ronis" <>
Subject   st: repeated measures ANOVA with missing observations
Date   Mon, 2 Dec 2002 11:50:12 -0500 (EST)

My experience with other software is that repeated measures ANOVA will
either drop cases with any missing data or fail to run when there are
missing data.  Before getting into more complex procedures like SAS PROC
MIXED I thought I'd give it a try in Stata.  My expectation was that the
failure would help motivate me for the work ahead.

I studied Kenneth Higbee's FAQ a bit at

My data are nicely organized in the long form with one observation per

The main purpose is to compare the performance of two different machines
for measuring fitness among sedentary pregnant women.  One machine is
considered the gold standard.  The women go through as many as five stages
of testing (changing the slope and/or speed of the treadmill).  For
reasons of safety the women are not allowed to overexert.  Of the 10 women
in the study, only one was allowed to go up to stage 5. (So 90% missing
data within that level).

All factors other than personID are within-subjects aka repeated measures

The factors are

Machine (2 levels, all were tested on both machines)

Time in gestation (2 levels, 18 wks or 28 wks, with some tested only once)

Stage of exercise (5 levels, with Stage 1, 2, and 3 for all (or almost
all), stage 4 missing for about a quarter, and stage 5 missing for 90%)

Arrangement of the data is
id, time, stage, machine, dv1: vo2 (volume of oxygen exhaled), other dvs

To my surprise, the following code ran and gave results that seemed
reasonable (given my eyeballing the data and means):

capture log close
log using preeval2.log, replace
* Approach from Higbee FAQ
set matsize 800
set memory 4m
set more off
use e:\yeo2\vo2-pree-val.dta

anova vo2 id time / time*id stage / stage*id machine / machine*id  /*
 */  time*stage / time*stage*id   /*
 */  time*machine  / time*machine*id   /*
 */  stage*machine / stage*machine*id  /*
 */  time*stage*machine /       ,  /*
 */  repeated (time stage machine)

I'm wondering whether this is really an appropriate analysis, and what
assumptions it / I may be making (especially unusual ones)?  For sig test
results I'm looking at the adjusted ones, not those in the initial ANOVA
table.  It has been about 20 years since I studied ANOVA.


David Ronis alias Offices in Ann Arbor, MI
 University of Michigan and Department of Veterans Affairs
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