Interaction plot of medians

Hello,

I would like to generate an interaction plot for studying the effects of a number of categorical variables, but using sample medians as opposed to the means. I started by modifying the interactionplot.m code by replacing calls to mean or nanmean with the median equivalents, and 'mean' with @median at line 298:

[interact,num] = grpstats(y,{factor1,factor2}, {@median,'numel'});

but I get the error: ??? Error using ==> interactionplotmed>plotaninteraction at 305 Some combinations of factor levels are missing.

Error in ==> interactionplotmed at 164
                plotaninteraction(ybar,group{j},group{i},varnames{j},varnames{i},...

Error in ==> intrcPlot at 144
interactionplotmed(Y,GROUP,'varnames',VARNAMES);

since my design matrix is atypical - one category (wavelet family) is only combined with certain levels of subcategories (wavelet number, wNum, and decomposition level, J). For the Db family (wType = 1) I am testing 10 sublevels (wNum = 1:10), while for the Coif family (wType = 2) there are 5 sublevels (wNum = 1:5), and for the Sym family there are 7 (wNum = 1:7). The number of levels of J is in turn dependent on wNum. For example, the design matrix for Db wavelets is: dFFdb2_6 = fullfact([2 2 4 1 3 8]);

          dFFdb8_14 = fullfact([2 2 4 1 4 7]);
          [dm,~] = size(dFFdb8_14);
          dFFdb8_14 = dFFdb8_14 + [zeros(dm,4) 3*ones(dm,1) zeros(dm,1)];

          dFFdb16_20 = fullfact([2 2 4 1 3 6]);
          [dm,~] = size(dFFdb16_20);
          dFFdb16_20 = dFFdb16_20 + [zeros(dm,4) 7*ones(dm,1) zeros(dm,1)];

          dFFdb = [dFFdb2_6; dFFdb8_14; dFFdb16_20];

with similar ones for Coiflets and Symlets. The Db, Coif, and Sym design matrices are then stacked into one large matrix to evaluate all combinations of variables in my algorithm.

I am able to generate interaction plots in JMP easily enough, but these use the sample means and I don't believe there is a way of modifying it to use the medians.

Any help is much appreciated. Thanks!

Phil

Answer 1

[Tom Lane]

It is true that interactionplot wants all factor combinations present. Here's a little script that will plot medians as functions of two predictors without that restriction. Maybe you can adapt it to your problem.

load carsmall
[med,grps] = grpstats(MPG,{Model_Year Origin},{@median 'gname'});

uyr = unique(grps(:,1));
uorg = unique(grps(:,2));
n1 = length(uyr);
n2 = length(uorg);
y = nan(n1,n2);

for j=1:length(med)
    [~,i1] = ismember(grps{j,1},uyr);
    [~,i2] = ismember(grps{j,2},uorg);
    y(i1,i2) = med(j);
end

plot((1:n1)',y,'o-')
xlim([.5,n1+.5])
set(gca,'xtick',1:n1,'xticklabel',uyr)
legend(uorg)

[Phil]

Perfect, thank you!