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Thanks for your time. I want to compare accuracy of several predicting models. I am comparing their MAE. each model use same all or some predictors. Which approach is better MANOVA or repeated measure ANOVA? Why?

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MANOVA and repeated measure ANOVA are used in very different situations. A MANOVA is a multivariate ANOVA and is used when one has multiple (often correlated) dependent variables wants to look for differences amongst treatment groups in all dependent variables. A repeated measure ANOVA is used when there is a single dependent variable but one has multiple measurements of it for each subject. The repeated measure ANOVA is used to separate within- and across-subject variability within a treatment group. It's hard to tell from the information supplied if a repeated measure ANOVA is what you want, but if you only have one dependent variable (in your case MAE) then you won't be able to use a MANOVA.

All that said, if you're doing model selection, you should probably penalize the models that use more parameters with an information theoretic approach like AIC or BIC.

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Fouad is not completely wrong. Textbooks commonly recommend either repated measures ANOVA or MANOVA for designs with within-subjects factors, depending on e.g., the amount of sphericity deviation. However, I fully agree that it is very hard to understand why one should use either of those from what he/she describes. – Henrik Dec 5 '12 at 19:28
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As I do not understand the question, as it stands at the moment, I can't tell which model is better. However, I do not completely agree with your first sentence. As @Henrik said, MANOVA was suggested as an alternative to RM ANOVA when the sphericity assumption is not met; it has its caveats as do Greenhouse and Geisser or Huynh-Feldt corrections. So, these two methods are not necessarily so different. For more information, I like to refer to A Bluffer’s Guide to ... Sphericity (PDF) and An introduction to sphericity. – chl♦ Dec 5 '12 at 21:40
I based the beginning of my answer off definitions of the MANOVA such as "The purpose of MANOVA is to test whether the vectors of means for the two or more groups are sampled from the same sampling distribution." found here or "Multivariate analysis of variance (MANOVA) is simply an ANOVA with several dependent variables" here. The bigger issue though, is that the OP probably does not want either. – Mimshot Dec 5 '12 at 22:11
@chl Thanks for the great links (+1). – Henrik Dec 6 '12 at 14:19

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