# Re: [R] logistic regression

From: <Bill.Venables_at_csiro.au>
Date: Wed, 25 Jun 2008 10:17:16 +1000

I find 3-factor interactions are about as much as I can think about without getting a bit giddy. Do you really need 4- and 5-factor interactions? If so, your only option is to get more data.

Bill Venables
CSIRO Laboratories
PO Box 120, Cleveland, 4163
AUSTRALIA

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-----Original Message-----
From: r-help-bounces_at_r-project.org [mailto:r-help-bounces_at_r-project.org] On Behalf Of Mikhail Spivakov
Sent: Wednesday, 25 June 2008 9:31 AM
To: r-help_at_r-project.org
Subject: [R] logistic regression

Hi everyone,

I'm sorry if this turns out to be more a statistical question than one specifically about R - but would greatly appreciate your advice anyway.

I've been using a logistic regression model to look at the relationship between a binary outcome (say, the odds of picking n white balls from a bag
containing m balls in total) and a variety of other binary parameters:

> a.fit <- glm (data=a, formula=cbind(WHITE,ALL-WHITE)~A*B*C*D,
> family=binomial(link="logit"))
> summary(a.fit)

glm(formula = cbind(SUCCESS, ALL - SUCCESS) ~ A * B * C * D family = binomial(link = "logit"), data = a)

Deviance Residuals:
[1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Coefficients:

```	Estimate	Std.	Error	z value	Pr(>|z|)
(Intercept)	-0.69751	0.02697	-25.861	<2.00E-16	***
A	-0.02911	0.05451	-0.534	0.593335
B	0.39842	0.06871	5.798	6.70E-09	***
C	0.829	0.06745	12.29	<2.00E-16	***
D	0.05928	0.11133	0.532	0.594401
A:B	-0.44053	0.13807	-3.191	0.001419	**
A:C	-0.49596	0.13664	-3.63	0.000284	***
B:C	-0.62194	0.14164	-4.391	1.13E-05	***
A:D	-0.4031	0.2279	-1.769	0.076938	.
B:D	-0.60238	0.25978	-2.319	0.020407	*
C:D	-0.58467	0.27195	-2.15	0.031558	*
A:B:C	0.5006	0.27364	1.829	0.067335	.
A:B:D	0.51868	0.4683	1.108	0.268049
A:C:D	0.32882	0.51226	0.642	0.520943
B:C:D	0.56301	0.49903	1.128	0.259231
A:B:C:D	-0.32115	0.87969	-0.365	0.715059

```
```---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 2.2185e+02  on 15  degrees of freedom
Residual deviance: 1.0385e-12  on  0  degrees of freedom
AIC: 124.50

Number of Fisher Scoring iterations: 3

_________________________________________________________________

This seems to produce sensible results given the actual data.
However, there are actually three types of balls in the experiment and I
need to model the relationship between the odds of picking each of the
type
and the parameters A,B,C,D. So what I do now is split the initial data
table
and just run glm three times:

>all

[fictional data]

TYPE WHITE ALL A B C D
a	100	400	1	0	0	0
b	200	600	1	0	0	0
c	10	300	1	0	0	0
....
a	30	100	1	1	1	1
b	50	200	1	1	1	1
c	20	120	1	1	1	1

> a<-all[all\$type=="a",]

> b<-all[all\$type=="b",]
> c<-all[all\$type=="c",]
> a.fit <- glm (data=a, formula=cbind(WHITE,ALL-WHITE)~A*B*C*D,
> family=binomial(link="logit"))
> b.fit <- glm (data=b, formula=cbind(WHITE,ALL-WHITE)~A*B*C*D,
> family=binomial(link="logit"))
> c.fit <- glm (data=c, formula=cbind(WHITE,ALL-WHITE)~A*B*C*D,
> family=binomial(link="logit"))

But it seems to me that I should be able to incorporate TYPE into the
model.

Something like:

>summary(glm(data=example2,family=binomial(link="logit"),formula=cbind(W

HITE,ALL-WHITE)~TYPE*A*B*C*D))

[please see the output below]

However, when I do this, it does not seem to give an expected result.
Is this not the right way to do it?
Or this is actually less powerful than running the three models
separately?

Will greatly appreciate your advice!

Many thanks
Mikhail

-----

Estimate	Std.	Error	z value	Pr(>|z|)
(Intercept)	-8.90E-01	1.91E-02	-46.553	<2.00E-16
***
TYPE1	1.93E-01	2.47E-02	7.822	5.18E-15	***
TYPE2	1.19E+00	2.42E-02	49.108	<2.00E-16	***
A	1.89E-01	3.34E-02	5.665	1.47E-08	***
B	1.60E-01	4.41E-02	3.627	0.000286	***
C	2.24E-02	4.91E-02	0.455	0.64906
D	1.96E-01	6.58E-02	2.982	0.002868	**
TYPE1:A	-2.19E-01	4.59E-02	-4.759	1.95E-06	***
TYPE2:A	-9.08E-01	4.50E-02	-20.178	<2.00E-16	***
TYPE1:C	2.39E-01	5.93E-02	4.022	5.77E-05	***
TYPE2:B	-1.82E+00	6.46E-02	-28.178	<2.00E-16	***
A:B	-2.26E-01	8.52E-02	-2.649	0.008066	**
TYPE1:C	8.07E-01	6.27E-02	12.87	<2.00E-16	***
TYPE2:C	-2.51E+00	7.83E-02	-32.039	<2.00E-16	***
A:C	-1.70E-01	9.51E-02	-1.783	0.074512	.
B:C	-3.01E-01	1.12E-01	-2.698	0.006985	**
TYPE1:D	-1.37E-01	9.20E-02	-1.489	0.136548
TYPE2:D	-1.13E+00	9.19E-02	-12.329	<2.00E-16	***
A:D	-2.11E-01	1.27E-01	-1.655	0.097953	.
B:D	-2.15E-01	1.55E-01	-1.387	0.165472
C:D	-5.51E-01	2.76E-01	-1.997	0.045829	*
TYPE1:A:B	-2.15E-01	1.17E-01	-1.84	0.065714
.

TYPE2:A:B	7.21E-01	1.28E-01	5.635	1.75E-08
***
TYPE1:A:C	-3.26E-01	1.24E-01	-2.643	0.008221
**
TYPE2:A:C	9.70E-01	1.53E-01	6.36	2.02E-10
***
TYPE1:B:C	-3.21E-01	1.38E-01	-2.321	0.020313
*
TYPE2:B:C	1.35E+00	1.89E-01	7.133	9.85E-13
***
A:B:C	1.80E-01	2.11E-01	0.852	0.394425
TYPE1:A:D	-1.92E-01	1.83E-01	-1.05	0.293758
TYPE2:A:D	6.76E-01	1.80E-01	3.75	0.000177
***
TYPE1:B:D	-3.87E-01	2.16E-01	-1.796	0.072443
.
TYPE2:B:D	1.09E+00	2.30E-01	4.709	2.49E-06
***
A:B:D	1.92E-01	2.73E-01	0.702	0.482512
TYPE1:C:D	-3.33E-02	3.18E-01	-0.105	0.916465
TYPE2:C:D	1.20E-01	5.05E-01	0.238	0.811914
A:C:D	-7.37E+00	1.74E+04	-4.23E-04	0.999663
B:C:D	3.14E-01	4.92E-01	0.638	0.523254
TYPE1:A:B:C	3.21E-01	2.64E-01	1.218	0.223336
TYPE2:A:B:C	-8.43E-01	3.59E-01	-2.351	0.018747
*
TYPE1:A:B:D	3.27E-01	3.84E-01	0.85	0.3952
TYPE2:A:B:D	-6.59E-01	4.08E-01	-1.617	0.105883
TYPE1:A:C:D	7.69E+00	1.74E+04	4.42E-04	0.999648

TYPE2:A:C:D	-1.60E+01	3.48E+04	-4.58E-04	0.999634

TYPE1:B:C:D	2.49E-01	5.70E-01	0.437	0.662288
TYPE2:B:C:D	-7.08E-01	8.97E-01	-0.789	0.430007
A:B:C:D	9.08E-03	2.47E+04	3.67E-07	1
TYPE1:A:B:C:D	-3.30E-01	2.47E+04	-1.34E-05	0.999989
TYPE2:A:B:C:D	1.10E+00	4.94E+04	2.22E-05	0.999982
--
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