Equivalent code to regress(), using fitglm()

Given the same input data, I would expect

b = regress(log(Y),[ones(size(X,1),1) X]);

and

mdl = fitglm(X,Y,'Link','log');
B = mdl.Coefficients.Estimate;

to give the same coefficients.

Below is some sample code where they do not. Am I missing something simple?

NTRIALS = 31;

dateString = {'01-04-1993','01-07-1995','01-03-1996','01-03-1997', ...
              '01-02-1998','01-07-1998','01-11-1998','01-08-1999', ...
              '01-09-1999','01-09-2002','01-01-2006','01-03-2006', ...
              '01-02-2008','01-05-2008','01-10-2008','01-01-2010', ...
              '01-02-2010','01-03-2010','01-10-2011','01-11-2011', ...
              '01-01-2012','01-04-2012','01-03-2012','01-04-2012', ...
              '01-09-2012','01-09-2012','01-01-2012','01-01-2012', ...
              '01-04-2013','01-06-2013','01-02-2014'...
                                                                }';

ARR = [1.27 0.84  0.90  1.26 ...
       1.61 0.50  1.28  0.98 ...
       1.08 1.24  0.61  0.67 ...
       0.70 0.44  0.41  0.33 ...
       0.40 0.90  0.54  0.80 ...
       0.28 1.30  0.39  1.20 ...
       0.40 0.36  0.501 0.40 ...
       1.04 0.505 0.34      ]';

N   = [372  251  301  150  ...
        40  127  560  168  ...
       293   49 1651  942  ...
       104  267  257 1326  ...
      1272   29  1088  218  ...
        66  165  1106  120  ...
      1417 1234  1169 1083 ...
        80 1404  1331    ]';

dateNumber = datenum(dateString,'dd-mm-yyyy');
dateVector = datevec(dateNumber);

year  = dateVector(:,1);

[b,bint,r,rint,stats] = regress(log(ARR),[ones(NTRIALS,1) year]);

mdl = fitglm(year,ARR,'Link','log');
B = mdl.Coefficients.Estimate;

figure
hold on
h  = line(datenum({'1993-01-01','2014-01-01'}),exp(1).^[b(1)+b(2)*1994 b(1)+b(2)*2014]);
hg = line(datenum({'1993-01-01','2014-01-01'}),exp(1).^[B(1)+B(2)*1994 B(1)+B(2)*2014]);
set(h,'Color','r')
set(hg,'Color','g')
semilogy(dateNumber,ARR,'o')
axis tight
set(gca,'YLim',[0.1 2],'YTick',[0.2 0.4 0.6 0.8 1.0 1.5 2])
set(gca,'XTick',1994:2:2014)
datetick('x')

Answer 1

[Tom Lane]

I believe these are not the same. For the fitglm model we are saying that Y has a normal distribution whose log(mean) has a linear relationship with the predictors. Y could take on negative values in that case. For the regress model we are saying that the log of Y has a normal distribution whose mean has a linear relationship with the predictors. Y would have to be positive in that case.

[the cyclist]

Proving once again that I am not a statistician, but just play one on TV. Thanks for the clear explanation.