Multivariate profile analysis


 Profile analysis is most commonly used in two cases:


1)      Comparing the same dependent variables between groups over several time-points.

2)      When there are several measures of the same dependent variable (Ex. several different psychological tests that all measure depression).


Profile analysis uses plots of the data to visually compare across groups.  Following this, specific equations can be used to test for the significance of the various patterns or effects.


Profile analysis generally has more power than a corrected univariate test.

A screen shot of input window:


ScreenHunter_02 Jan. 03 21.03.gif

The above example of profile analysis is comparing two groups WAIS 4 test: information memory, similarity analog, arithmatic reasoning and picture comparison.


A sample output of this module is as below:



Multivariate profile analysis for: 
 Information memory                 
 Similarity analog                  
 Arithmatic reasoning               
 Picture comparison                 
 Group variable: GROUP
 Group levels: 0, 1
 t test for each individual variable
                     N1     Mean1 N2    Mean2        t df    P value
Information memory   28 11.892857 12 9.750000 2.292335 38 0.02751490
Similarity analog    28  9.321429 12 6.333333 2.409823 38 0.02090964
Arithmatic reasoning 28 11.357143 12 8.750000 2.508933 38 0.01649348
Picture comparison   28  7.678571 12 5.916667 2.277562 38 0.02846621
 Hotelling T square test for equal means
 N1 N2 T-square        F df1 df2    P value
 28 12 11.95053 2.751768   4  35 0.04331741
 Test for parallelism
 N1 N2 T-square         F df1 df2   P value
 28 12 1.179525 0.3724815   3  36 0.7733281
 Test for coincedence
 N1 N2 T-square        F df1 df2     P value
 28 12 10.56198 10.56198   1  38 0.002419657
 Test for flat profile
 Total SS    BSS df1      BMS     WSS df2      WMS        F      P value
   1934.4 432.25   3 144.0833 1502.15 156 9.629167 14.96322 1.310572e-08





In profile analysis, the data are usually plotted with time points, observations, tests, etc. on the x-axis, with the response, score, etc. on the y-axis.  These plots are then made into profiles—lines—representing the score across time points or tests for each group.


Profile analysis asks following basic questions about the data plots:


1)  Are the groups at equal levels across time points or measurements?

            2)  Are the groups parallel between time points or measurements?

            3)  Are the groups coincident between time points or measurements?

4)  Do the profiles exhibit flatness across time points or measurements?


If the answer to any of these questions is no (i.e. that specific null hypothesis is rejected) then there is a significant effect.  The type of effect depends on which of these null hypotheses is rejected.


Equal Levels and coincidence


Whether or not the profiles have equal levels is the most straightforward test in profile analysis.  The test is basically asking does one group score higher on average across all measures or time points? 


To evaluate equal levels, the grand mean of all time points or measures is calculated for each group.  Since all of the time points or scores are collapsed into a group mean, this a univariate test.  Essentially, this is equivalent to a between groups main effect. 


Here are a couple of graphs to help with visualization of equal levels and coincidence:


Graph 1.  Equal levels (coincident)—no between group main effects.















Graph 2.  Unequal levels (non-coincident)—between group main effects.















Graph 3.  Equal levels (non-coincident)—no between group main effects. 

Although these profiles are not coincident, the average response for each group is the same.





Flatness and parallelism are both multivariate tests which compare the multiple segments of the profile.  Here, a segment is simply the difference in the response between time points or dependent variables.  Therefore, the segment is equivalent to the slope of the line between two points on the x-axis.


The flatness null hypothesis is that the segments are 0, i.e. the slope of each line segment is zero and the profile is flat.  This is evaluated independently for each group, making this a within-subjects test.  If the line is not flat (any of the segments vary significantly from 0 then there is a within groups main effect of time-point, dependent variable, measure, etc. 





Parallelism is usually the main test of interest in profile analysis.  The test for parallelism asks whether each segment (slope) is the same across all groups.


Here are some graphs to illustrate the concept of parallelism as it is used here:


Graph 1.  Parallel—no within group/between group interaction















Graph 2.  Non-parallel—within group/between group interaction.


















The data used in profile analysis must be on the same scale.  If it is not, a z-score or other transformation may be necessary.  If responses are all on the same scale, no transformation is necessary.


Sample Size and Power


There must be more subjects in the smallest cell than the number of dependent variables as a rule of thumb.  Small sample size can affect power and the homogeneity of variance/covariance test. 





Multivariate normality

-  Not important if there are more subjects in the smallest cell than number of dependent variables and there are equal overall sample sizes

-  Otherwise, check for skewness and kurtosis of dependent variables and perform transformation if needed

-  All dependent variables should be checked for univariate and multivariate outliers


Homogeneity of Variance-Covariance matrices

-  If sample sizes are equal, this is usually not an issue

-  If sample sizes are unequal, then you need to test for homogeneity



-  It is assumed that the dependent variables are linearly related to one another

-  Scatter plots of the dependent variables can be used to assess linearity

-  When dependent variables are normal and sample size is large this is not an issue