Example Session using logist

logist performs logistic regression.

» help logist

LOGIST Fit logistic regression model.
	[BETA,MU,DEV,DF,SE]=LOGIST(Y,N,X,OFFSET,PRINT)
	All input and output arguments except Y are optional.

	Y - response vector containing binomial counts
	N - number of trials for each count. Y is assumed to be binomial(p,N).
	X - matrix of covariates, including the constant vector if required
	OFFSET - offset if required
	PRINT - enter any argument if output required each iteration

	BETA - regression parameter estimates
	SE - associated standard errors
	MU - fitted values
	DEV - residual deviance
	DF - residual degrees of freedom

A simple logistic regression. The counts are out of 10 in each case and there is one covariate.

» y=[2 0 3 1 5 5 6 9 5 9];
» n=[10 10 10 10 10 10 10 10 10 10];
» x=(1:10)';
» X=[ones(10,1) x]
X =
     1     1
     1     2
     1     3
     1     4
     1     5
     1     6
     1     7
     1     8
     1     9
     1    10
» [beta mu dev df se]=logist(y,n,X)
beta =
   -2.5800
    0.4202

mu =
    1.0342
    1.4936
    2.1092
    2.8921
    3.8249
    4.8530
    5.8937
    6.8602
    7.6884
    8.3507

dev =
   13.5505

df =
     8

se =
    0.5839
    0.0923

Here is the same regression using a different statistical program, namely R. The same results are obtained.

> y <- c(2,0,3,1,5,5,6,9,5,9);
> n <- rep(10,10);
> x <- 1:10
> out <- glm(y/n ~ x,family=binomial,weights=n)
> summary(out)

Call:
glm(formula = y/n ~ x, family = binomial, weights = n)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.8472  -1.0761   0.3411   0.7306   1.6120  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)    
(Intercept) -2.58000    0.58390  -4.419 9.94e-06 ***
x            0.42020    0.09228   4.554 5.27e-06 ***
---
Signif. codes:  0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 40.848  on 9  degrees of freedom
Residual deviance: 13.551  on 8  degrees of freedom
AIC: 39.455

Number of Fisher Scoring iterations: 4

References

Collett, D. (2002). Modelling Binary Data, 2nd edn. Chapman & Hall, London.