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I have problem with homogeneity of regression slopes in ANCOVA. I have two species of snakes and I want to compare their tail lengths (dependent variable), that are dependent on body length (in ANCOVA used as covariate). Other ANCOVA assumptions are met, but there exist significant interaction between species*bodylength (intercepts are comparable, slopes are different).

Andy Field´s SPSS guide tells that broken assumption of homogeneity of regression slopes could be cast aside using multilevel statistic model. I´m trying to correctly run this analysis whole day, but I am unable to do it. Problem is that I want to compare tail lengths between species, which is my top of hierarchy (at the bottom are individual specimen). Do I have to set variable species as subject (assuming some hierarchy)?

Undoubtely I have to set body length as covariate and tail length as dependent variable. How can I compare my groups (species) independently of slopes (slopes are random)? What should be set as fixed factors and what random factors in SPSS? Field´s guide also tells that for mixed model analysis there is bug (version 17.0) related to factors dialog box such that categorical variables (in this case my species variable) should be put into covariate box (at least if it is bivariate). Is he right? I know what I want to do but dont know how to do it.

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Could you describe what you are doing precisely (which dialog box, etc.)? My – possibly outdated – understanding was that multilevel models were not available through the GUI in SPSS. For step-by-step guides to the SPSS sides of things, see my answer to stats.stackexchange.com/questions/24662/… –  Gala Apr 1 '12 at 7:47
    
Thank you for the links, but there is no answer to this type of question, I have two predictors, no repeated measures and I´m not interested in relationship body length - tail length between groups independently of slopes. I want to compare difference between tail lengths in my groups but filtering out body length (which is highly correlated with tail length but my species tail growth rate is different - so the slopes differ and I cannot use ANCOVA/or I can but with caution and help with scatterplot). I have tried not only GUI but Syntax also, but I´m not sure how it should look like –  Noro Apr 2 '12 at 9:40
    
but if I´m interested in tail length difference between species, variable species should be Fixed factor (or else SPSS will not give me F and p values). –  Noro Apr 2 '12 at 9:44
    
What is your question exactly? If you want to know more about SPSS implementation of multilevel models, then the answer to the previous question is relevant, repeated measures or not, and that's why I pointed you to it. Now, how to best analyze your data is a different question that I did not even try to answer. –  Gala Apr 2 '12 at 15:20
    
my question is how to order SPSS 17.0 to run this multilevel test (comparing tail differences between species controlling for body length but ignoring that each species has different slope for tail growth). Is this syntax correct to do above mentioned test? Can I use the same variable as subject and as factor (or covariate) in one test? My syntax now looks somehow like this (SVL - body length, TL - tail length, Taxcode - species): –  Noro Apr 3 '12 at 12:45

3 Answers 3

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You could simply create interaction terms between your predictor (body length) and an indicator variable for the species (that is, species fixed effects). You would then regress your outcome (tail length) on the species fixed effects and the interactions terms. My coauthors and I detail this procedure in our paper, Broken or Fixed Effects?

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Most econometric textbooks, e.g. Greene, emphasize that the key assumption in FE estimators is that fixed effects enter additively, not multiplicatively. No surprise, then, that if effects enter multiplicatively, an estimator that assumes additive fixed effects gets the wrong answer, except by chance. Unfortunately most people don't read textbooks closely. PS This does not avoid the need for multilevel models, the latter are more efficient if interaction is random effect. The key is whether the estimator consistent with the assumptions we make. –  Fred May 9 '12 at 23:11
    
@Fred, this is yet another example of mixing up the "fixed effects" as understood by say biometricians (the linear predictor) and "fixed effects" as understood by economsits (the within estimator in a panel data model). Things are much simpler here, and don't really call for the complicated estimators. Charlie, +1. –  StasK Sep 6 '12 at 3:33

I think it is possible to code specie specific slopes using your data and enter them into your model. You said you have only 2 species so a multilevel specification may not be needed.

I have performed a multilevel analysis 1 time in SPSS (yes, not via the GUI but Syntax) but I do not know how it works with ANCOVA.

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If what you want is to compare de ADJUSTED means of tail length at a fixed covariate (in order to remove the effect of total size), it is necessary to run an ANCOVA as you have explained and did. However if the homogeneity of slopes do not apply to your data IT MEANS something that is biologically interesting, something like the length of the tail among species varies when comparing different sizes of snakes. One option will be to make a scatterplot, test the interaction covXspecies to see if the you have heterogeneity of slopes and then describe the differences using the scaterplot. Other option could be to make size categories of body length in order to remove influence of covariates on response variable and treat it as a fixed factor. You will have then a 2 way ANOVA with species and size category as fixed factors. then you migth be able to test for interaction between species and size which i think it is most interesting than just testing for differences among species. did it help?, please excuse my english!

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