Regression with several dummy variables

I have a cell type variable with 20000 rows and 700 columns. I present here an example of the first 9 columns:

    C1 C2      C3      C4      C5      C6      C7      C8      C9

A={ 0  0  0  13  16  11  17  26  12 %row 1 is irrelevant
   12  0  0  1  0  0  0  0  0
   13  0  0  0  1  0  0  0  0
   16  0  0  0  0  1  0  0  0
   18  0  0  0  0  0  1  0  0
   26  0  0  1  0  0  0  0       0
   41  0  0  0  0  0  0       1  0}

I am trying to perform a regression.

C1 is simply and ID code; C2 is my binary dependent variable y. C3 is a dummy variable x (the elements, 0 or 1, are numbers), whose coefficient β (and if possible standard deviation) I want to interpret. From C4 onwards I have dummy variables (here the elements, 0 or 1, are logicals) that I also want to include in my regression to control for certain effects.

I most likely should use fitlm or regress functions but I am not being successful. Can someone help me? Thank you very much.

[dpb]

Sounds hopeless, nearly, with the number of variables, but guess you'll not know until actually try.

First, are the dummy variables coded to be independent? That is, are the large number having come from fewer variables but of different levels or are they actually all separate effects?

[Maria]

The large numbers did come from fewer variables but of different levels.

Answer 1

[dpb]

Given the response to the previous question, should be just

y=A{1}(2:end,2);     % y response variable
x=A{1}{2:end,3:end}; x=[ones(size(x,1),1 x];  % predictor variables plus constant term 
[b,bint,~,~,stats] = regress(y,x);

As said, all will depend upon what the actual design matrix X'*X looks like when it's computed (actually not computed by Matlab, but the characteristics of same are what determines the covariances, estimabilities, etc., etc., etc., which are, of course all dependent upon the codings chosen being independent.)

[Maria]

thank you. I will try it. You missed a bracket right?

[dpb]

There's an extra opening paren -- started w/ cell2mat but if is a single cell don't need it. Wipe the opening '(' in front of the A 's...

[Maria]

Thanks.It gives this error: Error: ()-indexing must appear last in an index expression. I am trying to find another solution!

[dpb]

My old eyes can't tell the difference, sorry. First set is the curlies {} and the second the regular parens. That presumes size(A) is 1x1 cell like

>> A={rand(3,5)}
A = 
  [3x5 double]
>> y=A{1}(2:end,2)
y =
  0.5497
  0.9172
>>

Otherwise, need to know what

whos A

returns.

[Maria]

It gives this error: Warning: X is rank deficient to within machine precision. > In regress at 84. Do you know why? Thanks

[dpb]

Yep...as suspected would be the case given the number of dummy variables, at least one column is the same as another. It'll be very difficult to find an encoding that won't lead to the problem I'd guess.

You can always try

rank(x)

to get an estimate of how many problems you have...

I repeat the final synopsis from my initial answer --

...all will depend upon what the actual design matrix X'*X looks like when it's computed (actually not computed by Matlab, but the characteristics of same are what determines the covariances, estimabilities, etc., etc., etc., which are, of course all dependent upon the codings chosen being independent.)

It's that last phrase about being independent that's the rub.