I recommend mixed effects model, often called multilevel modeling or random regression model as well. I do not recommend repeated measures ANOVA as it is not as flexible as linear mixed effects model. You can start by reading Gueorguieva, R., & Krystal, J. H. (2004). Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry, 61(3), 310-317.

I also recommend Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling change and event occurrence. Oxford: Oxford University Press. they have a webpage With PowerPoint slides and youtube lectures that would be helpful as well: http://gseacademic.harvard.edu/~alda/

Good luck with your analysis. Gudmundur

I try to avoid repeated-measures ANOVA. It does not do a particularly good job of assessing growth, especially if the between-client variance changes over time, as it often does. Repeated measures also has fairly challenging assumptions.

With three occasions, I recommend a simple linear trajectory model. This kind of model (aka mixed-effects model, hierarchical linear model, growth model, latent growth model, etc.) is a data reduction tool that will synthesize your results into what is essentially a best-fit straight line for each client. Deviation from the best-fit line is treated as noise/error.

The intercepts and slopes of these lines have a study-wide mean and variance (usually assumed to be normally distributed). You can then use treatment or other pre-study variables as predictors of the slope and intercept. PROC MIXED in SAS does this easily, as does any SEM/Path-analysis software. A key advantage, too, is that it does not require listwise deletion for incomplete data. It uses all available data from all participants.

Hope this helps,

Pat

I recommend mixed effects model, often called multilevel modeling or random regression model as well. I do not recommend repeated measures ANOVA as it is not as flexible as linear mixed effects model. You can start by reading Gueorguieva, R., & Krystal, J. H. (2004). Move over ANOVA: progress in analyzing repeated-measures data and its reflection in papers published in the Archives of General Psychiatry. Archives of General Psychiatry, 61(3), 310-317.

I also recommend Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling change and event occurrence. Oxford: Oxford University Press. they have a webpage With PowerPoint slides and youtube lectures that would be helpful as well: http://gseacademic.harvard.edu/~alda/

Good luck with your analysis. Gudmundur

I suggest you this nice paper at the following link::

http://www.jmir.org/2013/6/e113

Suggest the book "Discovering statistics using SPSS for Windows", Andy Field

In my view repeated measures ANOVA would probably be the most appropriate analysis, unless you have a particular reason for wanting to do something else. If you do not have any covariates or factors, i.e. only the response variable measured on three occasions for each patient, then a distribution-free test would be Friedman's test (also known as Friedman's two-way Analysis of Variance).

My preferred method unfortunately has one hardly achievable premise: the measurement instrument must fit the Rasch-Model. But if this is the case you could use a Linear Logistic Test Model for change.

As an example I suggest: http://jeb.sagepub.com/content/36/1/33.abstract doi: 10.3102/1076998610366260

Depending on your data (and research questions), I would suggest considering the broad category of finite mixture models or latent structure models. Among these, Markov (Latent Transition) and Latent Growth models have been used to describe and account for change during and following treatment.

R offers several packages that can do this (for instance Depmix or Flexmix). I believe SAS has some add-ons for this. You can also use MPlus.

Thank you so much to everyone who gave suggestions. I will be going through the data shortly so I'll know more based on your feedback.

Lia, maybe you could use the MLwiN software for measuring the method that you want to do.

Lia -

I think it would help to know what statistical package(s) you are working with or have available to you. It would be easier, then, to help you with your question. The mixed-effects models are certainly the way to go, however, whatever package you have available. I most certainly agree wiht Pat's comments about the assumptions needed to make a repeated measures anova useful. Any good mixed model package would allow you to tailor the covariance assumptions to fit your observed data and the questions you want to answer.

Thanks. I typically use SPSS... am in Australia working right now and that's what they have here too. Plan to learn R but haven't done so yet. Is that any help?

I suggest that its important to stick to what you understand and if you are not a statistician there is great benefit in selecting relatively simple mixed model or ANOVA approaches as they are transparent to you and any reviewer. These methods have the advantage of allowing you to look at the interaction of time with your other experimental factors. Repeated measures does not do this, or if it can I am unaware of how to go about it.

Whether you have to resort to RM is also often not entirely clear cut and the advice you get from different statisticians will often vary, so I suspect there is an element of individual preference. I have used RM in cases where I analysed metabolite concentrations in time series blood samples from repeatedly sampled sheep. This is a clear case of repeated measures as there may be differences between the individual sheep that cause differences in blood metabolite concentration that has nothing to do with my experimental treatment. There have been other instances where I have analysed chemical composition in whole leaf or stem samples taken at regular intervals from repeatedly sampled plants (I work on Miscanthus and for many genotypes one leaf or one stem constitutes only a very very minor portion of the plant). In these cases it is not so clear whether you need to use RM and it can be argued that each leaf/ stem is independent.

If I can avoid RM I do as it does not provide the depth of information I get from ANOVA or REML.

To add to your previous post, if you decide to learn R then you can start with using one of their user-designed Graphic User Interfaces. This greatly facilitates the learning process as you get something that is in-between SPSS and the traditional command-line interface R. I personally use (and recommend) RCommander, Deducer and RStudio. I'm at a point where I can run all of my analyses in R and have never looked back, and I'm no statistician. The difficulty of learning R has been overestimated IMO.

Depending on the type of data you have my recommendations may change a bit (if you have large N latent growth models may be the way to go). Without knowing much in the way of details, I would also recommend mixed linear models. SPSS handles those pretty easily.

You can use the Hotelling T2 test. You can find some details in Bernard Flury's book is called A Fisrt Couse in Multivariate Statistics. I run the simulate code for Hotelling T2 for the repeated measures data and I conclude that if the groups are correlated and non-homogene in variance sense you can use this test. Morever, your data does not satisyfy the multivariate normality, you can also use Hotteling T2 test for anaysis when the sample size is large(from Central limit and Slutsky Therom).

The data is pretty simple... ordinal and continuous data at baseline, 6 month follow up, 12 month follow up and 24 month followup. N of about 45. We want to know if preferred forms of play, amount spent etc changes at these intervals post treatment. It sounds like a majority of feel linear modeling is the way to go in SPSS?

Lia,

For analysis of treatment studies with a pre-treatment baseline and measurement on a limited number of post treatment occasions, I generally prefer to start with a mixed model ANCOVA, where I am modeling the post-treatment responses in two groups ( novel treatment versus control) adjusting (hence ANCOVA) for the baseline response. I differ from some of your respondents in that I like to treat "time" as a categorical measure, rather than imposing an assumption (e.g., linear change) on the post treatment responses (in the field I am working in, response to treatment is often rather prompt, with a limited amount of further change and then stability, so long as the treatment dose is fixed. With this form of the model, the main effect of treatment is a one degree of freedom test of whether the average of the baseline-adjusted post treatment differences across time points is non-zero, while the treatment x time interaction is a general test for variation in the magnitude of post treatment differences across time.

This differs from classic repeated measures ANOVA, the main effect of treatment averages treatment differences across pre- and post-treatment differences, and so lacks a clear interpretation in terms of treatment effects. The treatment x time interaction is the test for treatment effects in repeated measures ANOVA; it is a multiple degrees of freedom test that looks for any variation among time points (including pre-post treatment and among post-treatment time points), and may have less power than the one degree of freedom test to detect a (relatively) constant post treatment difference in the model I use.

You mention that some of your dependent variables are ordinal. Ordinal variables with a relatively few levels (especially if a lot of subjects cluster at the lowest or highest level) can be hard to fit well with linear models, since predicted values can exceed the limits of the possible (e.g., if you use linear regression you can wind up predicting a score of 5.5 on a variable scored from 1 to 5). You may want to look into software for repeated measures ordinal logistic models, either by the generalized estimating equations (GEE) of Liang and Zeger (I believe SPSS can support this), or generalized linear mixed models (PROC GLIMMIX in SAS, for example). Scott Menard, Applied logistic regression analysis, 2nd edition, Sage publications has a useful introduction to the general concepts of fitting ordinal logistic models, although he doesn't get into extensions to repeated measures.

I hope this helps.

Bob McMahon

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This helps a TON! Thanks so much!

Hi, Lia. As others have written, repeated measures ANOVA is not recommended b/c of nonindependence of observations and issues with missing data. I concur that Singer & Willett's Applied Longitudinal Data Analysis is a great resource--very understandable. In terms of software, I've had good luck with HLM. There's a free student version available that will easily handle your N, and the accompanying manual is pretty easy to follow: http://www.ssicentral.com/hlm/student.html

I would like to point out that the choice of analysis also depends on sample size and data quality in your investigation. I suspect that a longitudinal investigation looking at efficacy of psychological intervention will not have a very large sample size.

From own previous work, I can recommend the analysis of relative treatment effects (RTEs) by means of nonparametric ANOVA. You could look at it in our paper:

Lemche, E., et al. (2004). Mentalizing language development in a longitudinal attachment sample...Psychotherapy and Psychosomatics 73 (5): 366-374. In that paper you can find a link to the SAS model script that was used for analysis. The statistical methods used were described in a German language book: Brunner, E. & Langer, F. (1999). Nichtparametrische Analyse longitudinaler daten. Munich, Germany: R. Oldenbourg Verlag (ISBN 3-486-24915-0). It is quite nice output-wise, and automatically adjusts to missing data, so this is in each model per time point.

In case you have a very large sample size and a lot of interaction term, as mentioned above, latent growth curve models could be envisaged. The program package STATA 12 and higher has a handy SEM module. It has the advantage of not having to learn a programming language, and of quite intuitive and quick handling. Best of luck!

I agree with Patrick Malone. If you want to use R there is a nice summary in the last chapter of 'Multivariate analysis in R" by Everitt & Torsen, Springer, Use R series.

Dear Nower,

Repeated measure analysis of variance is a good statistic method for your research, but you may also performed multi-level regression techniques using by MLwiN software (Rasbash, Steele, Browne, & Goldstein, 2009).

Multi-level regression is the choice of statistical analysis when the data take the form of a hierarchical nature (see Singer & Willett, 2003).

Best wishes

If your sample is relatively small and you have access to a lot of data points (measurements over time, say session-to-session),  you could use methods derived from Markov models. The depmixS4 package in R has interesting functionality for this purpose.