Estimates missing values in repeated measurements (M.G. Kenward & R.W. Payne).
Options
PRINT = string tokens |
Controls output from the procedure (meanprofiles); default * i.e. none |
|---|---|
GROUPS = factor |
Factor indicating the plot on which each sequence of observations was made |
ORDER = scalar |
Order of ante-dependence structure (i.e. number of past times for which to adjust) |
Parameters
DATA = variates |
Observations at each time |
|---|---|
NEWDATA = variates |
Data variates with missing observations replaced by their estimates |
MEANPROFILE = tables |
Estimated mean profiles at each time |
Description
Suppose that we have a set of experimental units, or plots, within which observations are made in several locations at a sequence of times. Data from some of the locations may be missing at various times. The observed data values are specified in separate variates, one for each time point, using the DATA parameter. The factor identifying the experimental unit on which each observation was made is specified using the GROUPS option.
ANTMVESTIMATE assumes that the data have an ante-dependence (AD(r)) covariance structure whose order can be specified using the ORDER option; if this is not set, ANTMVESTIMATE takes the maximum possible order, number of times minus one. Using this assumption, ANTMVESTIMATE estimates the missing values and calculates the mean profiles for each unit. These can be saved, in tables indexed by the GROUPS factor, using the MEANPROFILES parameter, or printed by setting the PRINT option to meanprofiles. Also, the NEWDATA parameter allows new variates to be saved with the missing values replaced by their estimates.
Options: PRINT, GROUPS, ORDER.
Parameters: DATA, NEWDATA, MEANPROFILE.
Method
The algorithm in the procedure is a first-order approximation to maximum likelihood estimation which has the advantage of requiring only one pass through the data. At each time point, current plot means are estimated using the equations of maximum likelihood under an AD(r) covariance structure. The calculations required are simply those of analysis of covariance with previous individual measurements as covariates. Where previous measurements are missing they are replaced by previously estimated mean values and if there are no previous missing values the estimated plot means are full maximum likelihood estimates. The procedure uses a single pass through the time points. If the whole cycle were iterated to convergence joint maximum likelihood estimates of all the plot means would be obtained. Full details are given by Kenward (1994).
Action with RESTRICT
Any restriction on the data variates will be cancelled and a warning printed.
Reference
Kenward, M.G. (1994). The estimation of mean plot profiles and the identification of atypical plots using incomplete sequences of porous cup nitrate levels. Rothamsted Technical Report written for ADAS Biometric Unit, Cheltenham.
See also
Procedures: ANTORDER, ANTTEST, MULTMISSING.
Commands for: Repeated measurements.
Example
CAPTION 'ANTMVESTIMATE example',\
!t('Blood pressures of rats treated with various doses',\
'of Halothane following an induced mycocardial infarction.');\
STYLE=meta,plain
FACTOR [NVALUES=43; LEVELS=!(0,.25,.5,1)] Dose
VARIATE [NVALUES=43] Bloodpr[1,5,10,15,30,60,120,180,240]
READ Dose,Bloodpr[]
0.00 112.5 100.5 102.5 102.5 107.5 107.5 95.0 102.5 100.5
0.00 92.5 102.5 105.0 100.0 110.0 117.5 97.5 102.5 112.5
0.00 110.0 130.0 115.0 105.0 112.5 110.0 115.0 102.5 92.5
0.00 97.5 97.5 80.0 82.5 82.5 102.5 100.0 95.0 95.0
0.00 90.0 70.0 85.0 85.0 92.5 97.5 107.5 97.5 90.0
0.25 115.0 115.0 107.5 107.5 112.5 107.5 112.5 107.5 107.5
0.25 125.0 125.0 120.0 120.0 117.5 125.0 122.5 120.0 120.0
0.25 95.0 90.0 95.0 90.0 100.0 107.5 100.0 100.0 92.5
0.25 87.5 65.5 85.0 90.0 105.0 90.0 85.0 87.5 100.0
0.25 97.5 92.5 57.5 55.0 90.0 97.5 110.0 115.0 105.0
0.25 102.5 130.0 85.0 80.0 127.5 97.5 117.5 102.5 127.5
0.50 107.5 107.5 102.5 102.5 102.5 97.5 98.5 102.5 92.5
0.50 100.0 105.0 105.0 105.0 110.0 110.0 115.0 107.5 105.0
0.50 95.0 97.5 90.0 100.0 100.0 100.0 95.0 90.0 100.0
0.50 85.0 92.5 92.5 92.5 90.0 110.0 100.0 102.5 87.5
0.50 82.5 77.5 75.0 65.5 65.0 72.5 72.5 67.5 67.5
1.00 70.0 67.5 67.5 77.5 77.5 77.5 72.5 65.0 55.0
1.00 45.0 37.5 45.0 45.0 47.5 45.0 50.0 45.0 50.0
1.00 52.5 22.5 90.0 65.5 60.0 65.5 52.5 47.5 57.5
1.00 115.0 110.0 100.0 110.0 105.0 105.0 105.0 105.0 105.0
1.00 97.5 97.5 97.5 105.0 95.0 92.5 92.5 92.5 92.5
1.00 95.0 125.0 130.0 125.0 115.0 117.5 110.0 105.0 102.5
1.00 72.5 87.5 65.0 57.5 92.5 82.5 57.5 50.0 50.0
1.00 105.0 105.0 105.0 105.0 102.5 100.0 95.0 92.5 87.5
0.00 102.5 107.5 107.5 102.5 90.0 112.5 107.5 110.0 *
0.50 97.5 108.5 94.5 102.5 102.5 107.5 117.5 112.5 *
0.00 132.5 125.0 115.0 112.5 110.0 110.0 127.5 * *
0.25 90.0 87.5 97.5 95.0 100.0 95.0 102.5 * *
0.25 107.5 107.5 145.0 110.0 105.0 112.5 * * *
0.50 62.5 75.0 115.0 110.0 100.0 100.0 * * *
1.00 100.0 100.0 100.0 100.0 97.5 92.5 * * *
0.50 92.5 75.0 40.0 35.0 * * * * *
1.00 47.5 30.0 * * * * * * *
1.00 102.5 90.0 * * * * * * *
0.00 110.0 110.0 * * * * * * *
0.50 85.0 60.0 * * * * * * *
0.50 105.0 105.0 * * * * * * *
0.25 97.5 70.0 * * * * * * *
0.00 42.5 42.5 * * * * * * *
0.00 107.5 80.0 * * * * * * *
0.50 67.5 20.0 * * * * * * *
0.00 122.5 127.5 * * * * * * *
0.25 120.0 * * * * * * * * :
DREPMEASURES [TITLE='ignoring missing values'; GROUPS=Dose] Bloodpr
ANTMVESTIMATE [GROUPS=Dose] Bloodpr[];\
NEWDATA=Mvrepbp[1,5,10,15,30,60,120,180,240]
DREPMEASURES [TITLE='with estimated missing values'; GROUPS=Dose] Mvrepbp