Hi,
I have analysed my data using multivariate multiple regression (8 IVs, 3 DVs), and significant composite results have been found.
Before reporting my findings, I want to discuss in my results chapter (briefly) how the composite variable is created.
I have done some reading, and in the sources I have found, authors simply state that a 'weighted linear composite' or a 'linear combination of DVs' is created by SPSS (the software I am using).
They do not explain how they are weighted, and as someone relatively new to multivariate statistics, I am still unclear.
Are the composite DVs simply a mean score of the three DVs I am using, or is a more sophisticated method used on SPSS?
If the latter is true, could anyone either a) explain what this method is, or b) signpost some useful (and accessible) readings which explain the method of creating composite variables?
Many thanks,
Edward Noon
https://stats.stackexchange.com/questions/462505/how-does-spss-calculate-composite-variable-for-manova-multivariate-multiple-regr
https://www.statisticssolutions.com/directory-of-statistical-analyses-manova-analysis/
https://www.youtube.com/watch?v=3pzCa4Whv74&t=1s
You can find a PDF file with the algorithms for SPSS 26 on this page:
- https://www.ibm.com/support/pages/node/874712#en
HTH.
For the non SPSS users, What is a composite variable? Apologies, D. Booth
Hi David Eugene Booth - thank you for you for the response.
In MANOVA type analyses, my understanding is that for the multivariate F-tests, a composite or linear combination of the DVs in a model is created, and then the results determine whether each IV - when controlling for the effect of all other IVs in a model - is a significant predictor of the composite DV.
I have attached to this message the results I speak of, and hopefully this give you and/or others a better understanding of the results I mean: I am referring to the 'Multivariate Tests' at the top of this output.
Thank you, and any help would be greatly appreciated
Edward Noon, people who do not have SPSS installed will not be able to read that .spv file you uploaded. To make it more accessible, export (visible objects only) to some other format, such as PDF. HTH.
Sir, @David pls, for non SPSS users:
A composite variable is a variable created by combining two or more individual variables, called indicators, into a single variable [vector]. Composite variables are used to measure multidimensional concepts that are not easily observed. If necessary, weight can be plugged in for the composite average.
In R, you can use tidyverse to create a composite variable - see:https://www.google.com/url?sa=t&source=web&rct=j&url=https://m.youtube.com/watch%3Fv%3D5wgvw8VU1jE&ved=2ahUKEwj-u9DgwYTpAhUNuRoKHdiaDJwQFjAFegQIARAg&usg=AOvVaw2q4S3uKyUiwtX-7Fljh6wQ
And, to Edwards' question, I want to believe the variables combined linearly(additive) are independent and are vectors. The corresponding ordered elements were sum up giving a new vector variable.
See: https://www.google.com/url?sa=t&source=web&rct=j&url=https://m.youtube.com/watch%3Fv%3D3R-DUoSoV7I&ved=2ahUKEwiZoLeuwYTpAhVpyoUKHV46BiwQFjAHegQIDBAo&usg=AOvVaw17_hK8BF5wKuI6MMvDDY0u
Dear Edward Noon
thank you very much for your valuable question.
I agree with Cristian Ramos-Vera
BEst regards
OK.
MANOVA works by analysing a linear function of the DVs rather than the raw DVs. For example it could be
Ycomp = a*DV1 + b*DV2 + c*DV3
The weights a, b and c are optimised so that the variance explained in Ycomp by the DVs is maximised (as if in a one-way ANOVA).
This seems like a reasonable thing to do but it has some strange consequences. Firstly, its atheoretical so it might not be interpretable even if the separate DVs are. Second, it optimises on the data so will capitalise on sampling variability and other characteristics. Thus an identical replication using the same analysis will actually use a different composite DV. Third, standardised effect size statistic relate to the composite so are even harder to interpret than normal.
I'm not a fan of MANOVA for these and other reasons (e.g., it doesn't protect against Type I error in the way people assume).
Hi Thom Baguley - thank you for the response, it was extremely helpful.
So, am I right in thinking that this procedure is the same for both MANOVA and multivariate multiple regressions?
Many thanks
I would expect it to be analogous, but I haven't looked at multivariate regressions specifically.
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