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= How do I obtain an interaction in SPSS to describe how a fixed covariate influences a repeated measures interaction? = |
= How do I obtain an interaction in SPSS to describe how a fixed covariate influences a repeated measures interaction? = |
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| Let us suppose our four outcomes are NA1 to NA4 and suppose C1 is the age covariate. MANOVA will compute the interaction which is a difference of differences: (NA1-NA2)-(NA3-NA4) correlated with the covariate. | Let us suppose our four outcomes are NA1 to NA4 and suppose C1 is the age covariate (see the SPSS data file [attachment:covint.sav here.]). MANOVA will compute the interaction which is a difference of differences: (NA1-NA2)-(NA3-NA4) correlated with the covariate. |
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| ||||||||<style="TEXT-ALIGN: center"> '''Variation''' || '''SS''' || '''DF''' || '''MS''' || '''F''' || ||||||||<style="TEXT-ALIGN: center"> Correlation || || 0.1 || 0.3 || 0.5 ||} |
The Valence by Time Within subject effect ANOVA table has a term representing the Valence by Time by Covariate interaction (Regression) and a term representing the Valence by Time interaction adjusted for the covariate (Valence by Time). |
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| ||||||||||<style="TEXT-ALIGN: center"> '''Variation''' || '''SS''' || '''DF''' || '''MS''' || '''F''' || '''p''' || ||||||||||<style="TEXT-ALIGN: center"> Within Cells || 25.47 || 7 || 3.64 || || || ||||||||||<style="TEXT-ALIGN: center"> Regression || .03 || 1 || .03 || .01 || .929 || ||||||||||<style="TEXT-ALIGN: center"> Valence by Time || .00 || 1 || .00 || .00 || .991 || |
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| This is equivalent to a correlation between the difference of the differences representing the valence by time interaction:(NA1-NA2)-(NA3-NA4) and the covariate. | |
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The coefficients table shows the valence by time interaction adjusted for the covariate (Constant term) with the valence by time by covariate interaction (C1 term). These are identical to the terms in the ANOVA table outputted above by MANOVA. ||||||||||<style="TEXT-ALIGN: center"> '''Term''' || '''B''' || '''se''' || '''Beta''' || '''t''' || '''p''' || ||||||||||<style="TEXT-ALIGN: center"> Constant || -.042 || 3.394 || || -.012 || .991 || ||||||||||<style="TEXT-ALIGN: center"> C1 || -.125 || 1.349 || -.035 || -.093 || .929 || The same methods may be used for obtaining covariate by valence and covariate by time interactions. For example, to obtain the valence by covariate interaction in MANOVA we use the syntax below. {{{ COMPUTE NA13 = (NA1 + NA3)/2. COMPUTE NA24 = (NA2 + NA4)/2. manova NA13 NA24 with c1 c2 /wsfactors valence(2) time /wsdesign /print=transform signif(univ). }}} The analogous syntax for a correlation is given below. {{{ COMPUTE valenced = 0.5*(NA1+NA2)-0.5(NA3+NA4). REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT valenced /METHOD=ENTER C1 . }}} |
How do I obtain an interaction in SPSS to describe how a fixed covariate influences a repeated measures interaction?
Suppose we have a covariate, such as age, which does not vary with any levels of any repeated measures factors. We wish to see if age varies with time by valance interaction where each subject has their negative and positive moods (valence) assessed at two time points.
There are two equivalent ways to obtain the age by valence by time interaction using SPSS. Notice that the default repeated measures ANOVA procedure, GLM, will not compute this interaction because it can only handle one covariate for each subject.
The MANOVA procedure which is only available in SPSS syntax will compute this interaction but we need to use some trickery. MANOVA, unlike GLM, allows different (varying) covariates to be used for each level of the repeated measures.
Let us suppose our four outcomes are NA1 to NA4 and suppose C1 is the age covariate (see the SPSS data file [attachment:covint.sav here.]). MANOVA will compute the interaction which is a difference of differences: (NA1-NA2)-(NA3-NA4) correlated with the covariate.
Unfortunately MANOVA requires a covariate to be given for each combination of the levels of the repeated measures factors. MANOVA also correlates the difference representing the two-way valence by time interaction with the difference in the differences of the covariates. Putting these two pieces of information together we need to specify three more covariates, C2 to C4 which all equal zero.
Then (C1 - C2) - (C3 - C4) = C1 so that the difference in the differences of the covariates equals the covariate.
COMPUTE C2=0. COMPUTE C3=0. COMPUTE C4=0. manova NA1 NA2 NA3 NA4 with c1 c2 c3 c4 /wsfactors valence(2) time(2) /wsdesign /print=transform signif(univ).
The Valence by Time Within subject effect ANOVA table has a term representing the Valence by Time by Covariate interaction (Regression) and a term representing the Valence by Time interaction adjusted for the covariate (Valence by Time).
Variation |
SS |
DF |
MS |
F |
p |
||||
Within Cells |
25.47 |
7 |
3.64 |
|
|
||||
Regression |
.03 |
1 |
.03 |
.01 |
.929 |
||||
Valence by Time |
.00 |
1 |
.00 |
.00 |
.991 |
||||
This is equivalent to a correlation between the difference of the differences representing the valence by time interaction:(NA1-NA2)-(NA3-NA4) and the covariate.
COMPUTE naintd = (NA1-NA2)-(NA3-NA4). REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT naintd /METHOD=ENTER C1 .
The coefficients table shows the valence by time interaction adjusted for the covariate (Constant term) with the valence by time by covariate interaction (C1 term). These are identical to the terms in the ANOVA table outputted above by MANOVA.
Term |
B |
se |
Beta |
t |
p |
||||
Constant |
-.042 |
3.394 |
|
-.012 |
.991 |
||||
C1 |
-.125 |
1.349 |
-.035 |
-.093 |
.929 |
||||
The same methods may be used for obtaining covariate by valence and covariate by time interactions. For example, to obtain the valence by covariate interaction in MANOVA we use the syntax below.
COMPUTE NA13 = (NA1 + NA3)/2. COMPUTE NA24 = (NA2 + NA4)/2. manova NA13 NA24 with c1 c2 /wsfactors valence(2) time /wsdesign /print=transform signif(univ).
The analogous syntax for a correlation is given below.
COMPUTE valenced = 0.5*(NA1+NA2)-0.5(NA3+NA4). REGRESSION /MISSING LISTWISE /STATISTICS COEFF OUTS R ANOVA /CRITERIA=PIN(.05) POUT(.10) /NOORIGIN /DEPENDENT valenced /METHOD=ENTER C1 .