Dear Dorcas,

I am not entirely sure how your model looks like, but if published and reconstructed are your outcomes and you model stage and temp as fixed effects, your approach might be right. Concerning your second question: You will need to add an interaction term stage*temp and take a look at the least square means of the differences. Unfortunately I work with SAS in general, so I cannot help you with R precisely. Maybe this link helps (?):

https://cran.r-project.org/web/packages/phia/vignettes/phia.pdf

This looks like factorial ANCOVA to me. You can set this up in various ways, but one simple (but powerful) model is to use the change score (reconstructed - published) as outcome Y stage as a factor and temp and baseline (published) as covariates. This model has no repeated measures or DVs and assumes that published and reconstructed are on the same scale.

Interpretation is helped by entering temp and baseline.

It is MANOVA with 2 factor   stage and tem  .use another program   like GenestT 12 and use   dancan for comparison  between  means 

Thank you Ann Christina. That really helps. I included the interaction term followed by LSD but I am still getting an empty result.

Thom, Thanks. Yes, they are on the same scale. Let me try ancova and see.

Isam, that's exactly what I am asking. How to do it. Let me try what has been suggested

It could also be t - test (or Mann - Whitney). First, perform a factor analysis (or principal component analysis), create a factor of the three (dependent variables) and then compare means for the levels of the factor. T - test if the distribution of the factor is normal otherwise, Mann - Whitney.