Sunday, January 19, 2014

Profile analysis in SAS with R-generated figure

I was tickled to find a set of code to do a profile analysis in R hiding in a larger set of code examples.  A profile analysis is a multivariate ANOVA for repeated measures (Tabachnik and Fidell 2007).  I haven't been able to make the flatness test in SAS and R match yet using the code from the linked site, though the tests for parallelism and levels give the same results.  (I'll update the post if I figure that out).  Regardless, I really liked how the linked site made an interaction plot for a profile analysis, with pale lines for individuals shown in the background behind averages for each level.  So, what I've been doing for my profile analyses lately is using R to format the data, running the profile analysis in SAS and then graphing in R.

1. R code for formatting the data

My data are usually in column form, with each level and group as factors in two additional columns.  To get to the one-column-per-group needed for a profile analysis, I use the reshape2 package.  Follow the instructions in the melting post.  (I'll use that dataset here.)

Once you have your data in the correct format, you can export it to a .csv text file.  Make sure you have your workspace set to where you want the file to go.  (I usually do this step at the beginning when I import data, but since we generated our dataset in R, the workspace needs to be set here.)

#make sure you use two backslashes, not one.
write.csv(data.columns,file="20140116_profile_analysis.csv", na=".")
#Writes a file that can easily be imported into SAS.
#Note the na="." part, which gives periods for missing data as SAS prefers.
#My sample dataset doesn't have this, but I've left it in for when I do have a set with missing data.
#(SAS will not use those individuals in the profile analysis.)
#The file will be written to your working directory.
#You can now import it into SAS.


2. SAS code for analysis

The code is adapted with little change from Tabachnik and Fidell (2007), who also explain further tests you can do for your analysis.

proc glm data=whereyoukeepyourdata.dataset;
/*The profile analysis uses proc glm.*/
class levels;

/*In the class statement, levels is the variable name of you want your levels to be.*/model group1 group2 group3 group4 = levels;
/*The model statement tells you what you are testing. Here you want levels to be run on the four test grouping variables.*/
repeated teststimulus 4 profile; 

 /*This names the test1-4 variables (grouping/subtest/whatever you want to call it), so pick a descriptive name that will make interpreting your results easier.  The number after it (4) is how many groups you have.  The 'profile' turns it into a profile analysis */
title 'profile analysis';

/*This line is not required, but it makes the results easier to find if you are running more than one analysis.*/

 /*runs the test*/

Here is where you get the output.  I highlight the tests for flatness (gray), parallelism (blue), and levels (yellow),

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no teststimulus Effect
                             H = Type III SSCP Matrix for teststimulus
                                       E = Error SSCP Matrix

                                        S=1    M=0.5    N=2

          Statistic                        Value    F Value    Num DF    Den DF    Pr > F

          Wilks' Lambda               0.37200666       3.38         3         6    0.0955
          Pillai's Trace              0.62799334       3.38         3         6    0.0955
          Hotelling-Lawley Trace      1.68812389       3.38         3         6    0.0955
          Roy's Greatest Root         1.68812389       3.38         3         6    0.0955

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no teststimulus*levels Effect

                         H = Type III SSCP Matrix for teststimulus*levels
                                       E = Error SSCP Matrix

                                        S=1    M=0.5    N=2

          Statistic                        Value    F Value    Num DF    Den DF    Pr > F

          Wilks' Lambda               0.37476423       3.34         3         6    0.0975
          Pillai's Trace              0.62523577       3.34         3         6    0.0975
          Hotelling-Lawley Trace      1.66834432       3.34         3         6    0.0975
          Roy's Greatest Root         1.66834432       3.34         3         6    0.0975

The GLM Procedure
Repeated Measures Analysis of Variance

Tests of Hypotheses for Between Subjects Effects

        Source                      DF     Type III SS     Mean Square    F Value    Pr > F

        levels                          57.34512196     57.34512196      19.96    0.0021
        Error                           22.98499258      2.87312407

You then use the data from each to calculate your effect sizes.

Flatness  η2= 1 - lambda
η2= 1- 0.37200666
η2= 0.6279933

Parallelism partial η2= 1 - lambda ^ (1/2)
partial η2= 1- 0.37476423 ^ (1/2)
partial η2= 0.3878201

η2= SS between groups / (SS between groups + SS within groups)
η2= 57.34512196 / (57.34512196 + 22.98499258)
η2= 0.7138683

3. R code for figure

This is based on the U. Florida page that I mentioned above.

#First take the data.columns and add some information on any symbols or color scheme.
#Here I'm coloring the two levels and
#adding line types (even-numbered individuals are dashed, odd are solid).

data.columns$additional.linetype<-rep(c("solid", "dashed"), 5)

"group2", "group3", "group4",
"additional.linetype", "levels.color")]
#Make a small matrix with just the variables needed, using the melted dataset from step 1.
#I also include two additional variables for graphing: linetype and color.
#You can code these into a new column using your factors from the original dataset.

#Some objects need to be calculated for later plotting.
#This counts number of subscores/groups (test stimuli),
#but only the first four columns because the last two are not the data.

#Now you can create the main body of the figure.
matplot(1:p, t(as.matrix(figure.profile[,1:4])),
#1:p counts the groups, here used as the number of positions on the x-axis.
#t() transposes the matrix (created from the dataframe by as.matrix
#and using the column selection [,1:4] makes sure you only select the data columns
#and not our symbol information columns.
type="l", lwd=1, # says this is a line graph (type="l") with line width of 1.
#the line type is given by a variable in my dataset.
#In this case, it is not part of the profile analysis,
#but is there just for visual interpretation.
#You could also use different line types to represent
#the different levels instead of color.  
#That would be particularly good
#if you need a black-and-white figure for publication.
#as.numeric is needed for it interpret it correctly.
#Again, another symbol defined by a column in the dataset.
#I needed as.character to make sure it reads the factor as 
#characters, otherwise it (sometimes) gives an error
#depending on the data type in the column.

xaxt="n", #no x-axis (you'll be adding this manually soon)
main="Profile analysis",
xlab="Subtest/the repeated measurement/groups",

ylab="Dependent variable")

axis(1, 1:p, colnames(figure.profile[,1:4]))
# Add x-axis labels.
#1 is the position (the x-axis on bottom), 1:p says how many labels to add,
#and colnames takes the names from the dataset's grouping columns.
#You could also write replace colnames(figure.profile[,1:4]) with a list
#if your column names aren't tidy enough.
#axis(1, 1:p, c("Group 1", "Group 2", "Group 3", "Group 4"))

( <- by(figure.profile[,1:4], data.columns$levels, colMeans))

#Take the mean for each level across the columns 1:4 (the groups) of the matrix from above.
#The original code says to use mean but mean only works with vectors;
#colMeans works on a dataframe, which is what we have.
lines(1:p,[[1]], lwd=3, col="blue")
lines(1:p,[[2]], lwd=3, col="orange")

#These have thicker line widths (lwd=3 instead of 1) to make them stand out
#from the lines that we plotted to represent each sample.

legend("topleft", c("A", "B"), col=c("blue","orange"), lwd=3, title="Levels")
#If appropriate, add a legend to some position (here top left, but you can change this).

You now have significance tests for parallelism, levels, and groups (shown in the caption), and a clear figure showing the levels and groups for each sample and the averages.  (Your data will turn out a little different because the dataset was randomly generated in R, though the approximate differences should be the same since we set the means and standard deviations at the same values each time.)

There is no significant interaction between levels and groups (parallelism test) (Wilks' Λ=0.37, df=3,6, p=0.10, partial η2=0.39).  There is no significant difference between responses to the test groups (flatness test) (Wilks' Λ=0.37, df=3,6, p=0.10, η2=0.). There is a significant difference between levels (difference in levels test) (F1,8=19.96, p=0.002, η2=0.71).

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