How can put random effects in the formula of Fit linear mixed model?

Suppose we have the data set :

ID   Res  X1   X2   Z1   Z2
1     1   1.5  22   2.3  657
1     2   1.8  23   2.4  674
2     3   2.1  18   2.5  681
2     1   2.5  20   2.4  682
3     2   1.9  21   2.4  684
3     3   1.5  25   2.1  674
(ID: Id number, Res: Response, X1,X2: fixed effects, Z1,Z2: random effect)

To fit Y=XA+ZB I can use lme = fitlme(tbl,formula) in Matlab so I make the table

tbl=table(D(:,1),D(:,2),D(:,3),D(:,4),D(:,5),D(:,6),'VariableNames',{'Id','Response','FE1','FE2','RE1','RE1'});

Now to fit we need to use

lme = fitlme(tbl,'y ~ fixed + (random1|grouping1) + ... + (randomR|groupingR)');

So I put Response, FE1 and FE2 as y and fixed respectively:

lme = fitlme(tbl,'Response ~ FE1 + FE2 + (RF1|???)+(RF2|???)');

In the Matlab we need to use the grouping variables for the formula where the grouping variables can be categorical, logical, character arrays, or cell arrays of strings.

My question is how can make the grouping variables ?! or how put random effects RF1 and RF2 in the formula with respect my data? or which formula is correct for my data?

I do not understand why matlab needs to grouping variables?!

Bests Ali

Answer 1

[Gautam Pendse]

Have a look at the examples here:

http://www.mathworks.com/help/stats/fitlme.html

You can use "categorical" to work with categorical data. Have a look at this page:

http://www.mathworks.com/help/matlab/ref/categorical.html

Hope this helps,

Gautam