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Thanks to everyone who responded and those who though they didn't respond,
thought about it. Please find below the various suggestions by different
individuals.
-Jabulani
---------------------------
I wonder if you could treat this as a linear model with correlated errors
and follow the BUGS example Stagnant for a changepoint in linear
regression. It wouldn't be exactly the same, but perhaps a starting point.
A nonBayesian approach might treat this as an interrupted time series and
do an intervention analysis. Consult a time series text such as Enders
(1995), Applied Econometric Times Series, Wiley. A nice computer package
for analyzing times series is RATS, available from Estima. Also, the SAS
ETS package is available, but probably harder for an individual to
purchase.
(As an aside: One text that has a short, easy to read, introduction to
interrupted time series and intervention analyses is Cook and Campbell
(1979)
Quasi-Experimentation: Design and Analysis Issues for Field Settings.
It is publihsed by Houghton Mifflin, but might not be in print anymore.
Good Luck!
Laura Thompson
--------------------
It's not completely appropriate, I don't think, but in a paper I discuss
mixed effects models with two-piece linear splines for two distinct
periods.
It might be helpful. I'd be happy to discuss it with you further if you'd
like.
Kleinman, Ibrahim, and Laird (1998)
A Bayesian Framework for intent-to-treat analysis with missing data.
Biometrics v.54 p.265-278
Ken Kleinman
---------------------
A simple model comparison should do:
If Subj is a factor with a category identifying each subject uniquely,
PPI is a pre- post- intervention factor category 1 for measures before
intervention, 2 for measure after
(you will have to choose which the middle point is)
and Time is a continuous variable for the 5 time points.
Fit the models
Subj + PPI/Time to obtain deviance1 df1
and
Subj + PPI + Time to obtain deviance2 df2
The likelihood ratio Chi-squared test of the effect of intervention is
then:
Chi2 = (deviance2 - deviance1) with df = df2 - df1 ( 1 in this case)
The first model will supply you with
You will have to check Normality (use a Gamma error if positively skew
residuals, don't take logs)
and you should check the linearity of the time relationship - ignoring
non-linearity will introduce autocorrelation.
Yours Tony Swan
----------------------
The following should prove useful for your question re: modeling an
intervention with before and after information:
Good luck.
Julia McQuillan
University of Nebraska - Lincoln
Allison, Paul D. 1994. “Using Panel Data to Estimate the Effects of
Events.” Sociological Methods & Research. 23:2:174-199.
Cherlin, Andrew J., P. Lindsay Chase-Landsdale, Christine McRae. 1998.
“Effects of Parental Divorce on Mental Health Throughout the Life
Course. “ American Sociological Review. 63:239-249.
Davila, J., Karney, B.R. & Bradbury, T.N. 1999. Attachment change
processes in the early years of marriage. Journal of Personality and
Social Psychology. 76.738-802.
Karney, Benjamin R., Thommas N. Bradbury. 1995. “Assessing longitudinal
Change in Marriage: An Introduction to the Analysis of Growth Curves.”
Journal of Marriage and the Family. 57:1091-1108.
Karney, Benhamin R. and Thomas N. Bradbury. 1997. “Neuroticism, Marital
Interaction, and the Trajectory of Marital
Osgood, Wayne D. and Gail L. Smith. 1995. “Applying Hierarchical Linear
Modeling to Extended Longitudinal Evaluations: The Boys Town Follow-Up
Study.” Evaluation Review. 19:1:3-38.
Willett, John B. 1977. “Questions and Answers in the Measurement of
Change.” Review of Research in Education. 15:345-421.
------------------
Main refs:
Matthews, J.N.S., Altman, Douglas G., Campbell, M.J. and Royston, Patrick
Analysis of serial measurements in medical research. Br Med J,
1990;300:230-235.
Finney D. J. Repeated Measurements: what is measured and what repeats.
Statistics in Medicine, 1990; 9: 639-644
Frison L & Pocock SJ (1992) Repeated measures in clinical trials: analysis
using mean summary statistics and its implications for design. Statistics
in
Medicine; 11: 1685-1704
Paul T Seed ([log in to unmask])
Department of Public Health Sciences,
Guy's Kings and St. Thomas' School of Medicine,
King's College London,
5th Floor, Capital House 42 Weston Street, London SE1 3QD
tel (44) (0) 171 955 5000 x 6223
fax (44) (0) 171 955 4877
Tuesdays only:
Public Health Medicine, 11th Floor, North Wing,
St Thomas' Hospital, London SE1 7EH
tel (44) (0)171 928 9292 x 1511
"The line between good and evil passes not between one country and another,
nor between one political system and another, nor yet between one faith and
another - but it passes through the middle of every individual."
- Alexander Solzhenitsyn (attr.)
----------------
Anyway, I was actually interested in your message as well - i've been
recently helping someone analyse data similar to yours but with more
timepoints. They were using antedependence modelling (which is available
in Genstat with commands ANTORDER and ANTTEST) but this approach is
quite involved and is maybe not really necessary for as few as 5
timepoints. For 5 time points i would analyse as a split plot ANOVA,
where time is the split plot factor. This is not strictly valid (as time
is not randomised) but i think it's acceptable.
Don't know if this will help you at all - if you think it would, let me
know if you want more details. In any case i would be interested in any
comments or references you get off other people.
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