calculating logit parameters (odd ratio is exactly one or zero)

Dear statistician experts,

Sorry if this is a trivial question, or the old same question (i don't know
what is the efficient key word for this issue).
In order to understand the calculation of parameter of logistic regression,
  I did an exercise through spreadsheet following the procedural example
from a literature, or the available spreadsheet (with calculation formula).
I ended up with infinity (divided by zero) when the odd ratio is exactly 1
(FD=12) or invalid number when odd ratio is zero (MFD = 0) after log.
I am wondering  how R through GLM function (particularly logit or logistic
regression) treats the odds ratios or log odd ratios that is exatcly one or
zeros.

The sample data is like this:
#HH Fsize FD
1 1.29472 0
2 1.6184 0
3 2.4276 1
4 2.4276 2
5 20.23 2
6 1.6184 3
7 1.820 3
8 0.4046 3
9 6.069 4
10 2.6299 4
11 0.72828 5
12 2.4276 5
13 6.069 7
14 4.8552 7
15 2.32645 7
16 1.6184 8
17 1.0115 8
18 1.0115 8
19 5.2598 9
20 2.023 10
21 0.6069 10
22 1.2138 11
23 0.8092 11
24 1.4161 11
25 0.6069 11
26 3.440 11
27 1.2138 12
28 1.2138 12
29 0.4046 12
30 1.2138 12

Fsize is the farm size (acre or hectare).  Food deficit (FD) is the number
of months (last year from the survey took place) that an household had
bought food-grains (minimum = 0 month, maximum = 12 months or whole year
deficit).
Even though I "jitter"-ed the minimum or maximum FD value only (eg.
FD=0+1e-6 or FD=12-1e-6), nothing changed to the result.

The formula I used is like this:
--------------------------------------------------------------
glm(FD ~ Fsize, data = subFS)
--
Coefficients:
(Intercept)        Fsize
      7.7913      -0.3092

Degrees of Freedom: 29 Total (i.e. Null);  28 Residual
Null Deviance:      463
Residual Deviance: 425.5        AIC: 170.7
--------------------------------------------------------------

I appreciate for any clarification.

Best wishes,
Wim

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1. The formula you used is not for a logistic but an ordinal  
regression (since you are using the default gaussian family rather  
than family="binomial" or whatever.

2. R (nor any other software) can deal with perfect separation (nor  
quasi-separation) of classes, since the problem is not well defined  
in such a case as you found out already. R will give a warning in  
that case, that the Fisher Scoring does not converge.

LDA will give perfect results in such a case (well, unless the  
within class covariance matrix is singular).

Best,
Uwe Ligges



On 12.12.2011 11:46, wim nursal wrote:

Dear statistician experts,

Sorry if this is a trivial question, or the old same question (i  
don't know
what is the efficient key word for this issue).
In order to understand the calculation of parameter of logistic  
regression,
 I did an exercise through spreadsheet following the procedural  
example
from a literature, or the available spreadsheet (with calculation  
formula).
I ended up with infinity (divided by zero) when the odd ratio is  
exactly 1
(FD=12) or invalid number when odd ratio is zero (MFD = 0) after log.
I am wondering  how R through GLM function (particularly logit or  
logistic
regression) treats the odds ratios or log odd ratios that is  
exatcly one or
zeros.

The sample data is like this:
#HH Fsize FD
1 1.29472 0
2 1.6184 0
3 2.4276 1
4 2.4276 2
5 20.23 2
6 1.6184 3
7 1.820 3
8 0.4046 3
9 6.069 4
10 2.6299 4
11 0.72828 5
12 2.4276 5
13 6.069 7
14 4.8552 7
15 2.32645 7
16 1.6184 8
17 1.0115 8
18 1.0115 8
19 5.2598 9
20 2.023 10
21 0.6069 10
22 1.2138 11
23 0.8092 11
24 1.4161 11
25 0.6069 11
26 3.440 11
27 1.2138 12
28 1.2138 12
29 0.4046 12
30 1.2138 12

Fsize is the farm size (acre or hectare).  Food deficit (FD) is the  
number
of months (last year from the survey took place) that an household  
had
bought food-grains (minimum = 0 month, maximum = 12 months or whole  
year
deficit).
Even though I "jitter"-ed the minimum or maximum FD value only (eg.
FD=0+1e-6 or FD=12-1e-6), nothing changed to the result.

The formula I used is like this:
--------------------------------------------------------------
glm(FD ~ Fsize, data = subFS)
--
Coefficients:
(Intercept)        Fsize
     7.7913      -0.3092

Degrees of Freedom: 29 Total (i.e. Null);  28 Residual
Null Deviance:      463
Residual Deviance: 425.5        AIC: 170.7
--------------------------------------------------------------

I appreciate for any clarification.

Best wishes,
Wim

Dear Uwe and David,

Yes, definitely i was wrong.  The expression in R should be:

glm(cbind(FD, 12 - FD) ~ Fsize, family=binomial, data=subFS)
----
Call:  glm(formula = cbind(FD, 12 - FD) ~ Fsize, family = binomial,
     data = subFS)

Coefficients:
(Intercept)        Fsize
      0.6381      -0.1203

Degrees of Freedom: 29 Total (i.e. Null);  28 Residual
Null Deviance:      193.3
Residual Deviance: 179.9        AIC: 245.1
----

(the direction of Fsize is as expected).

I am not sure with your second statement mentioning that "R can deal with
perfect separation".

Despite of convergence issue, does R take into
account zero or infinite odds value or leave them to calculate the
parameters? How? I need to know the basic of this calculation since so far
I haven't found any literature discuss this problem and the way to handle
this (well, someone need to understand this as well :) )
David, i'm thinking to use LDA as well but i cannot comment this time.

Thanks for any clarification.

Best,
Wim

Research Officer
CIFOR-Indonesia













On Tue, Dec 13, 2011 at 4:08 AM, David Winsemius<dwinsemius at comcast.net>wrote:

On Dec 12, 2011, at 3:51 PM, Uwe Ligges wrote:

  1. The formula you used is not for a logistic but an ordinal regression

(since you are using the default gaussian family rather than
family="binomial" or whatever.

this this then produce one version of the "Armitage linear test of trend"?

2. R (nor any other software) can deal with perfect separation (nor
quasi-separation) of classes, since the problem is not well defined in such
a case as you found out already. R will give a warning in that case, that
the Fisher Scoring does not converge.

LDA will give perfect results in such a case (well, unless the within
class covariance matrix is singular).

Best,
Uwe Ligges



On 12.12.2011 11:46, wim nursal wrote:

Dear statistician experts,

Sorry if this is a trivial question, or the old same question (i don't
know
what is the efficient key word for this issue).
In order to understand the calculation of parameter of logistic
regression,
  I did an exercise through spreadsheet following the procedural example
from a literature, or the available spreadsheet (with calculation
formula).
I ended up with infinity (divided by zero) when the odd ratio is exactly
1
(FD=12) or invalid number when odd ratio is zero (MFD = 0) after log.
I am wondering  how R through GLM function (particularly logit or
logistic
regression) treats the odds ratios or log odd ratios that is exatcly one
or
zeros.

The sample data is like this:
#HH Fsize FD
1 1.29472 0
2 1.6184 0
3 2.4276 1
4 2.4276 2
5 20.23 2
6 1.6184 3
7 1.820 3
8 0.4046 3
9 6.069 4
10 2.6299 4
11 0.72828 5
12 2.4276 5
13 6.069 7
14 4.8552 7
15 2.32645 7
16 1.6184 8
17 1.0115 8
18 1.0115 8
19 5.2598 9
20 2.023 10
21 0.6069 10
22 1.2138 11
23 0.8092 11
24 1.4161 11
25 0.6069 11
26 3.440 11
27 1.2138 12
28 1.2138 12
29 0.4046 12
30 1.2138 12

Fsize is the farm size (acre or hectare).  Food deficit (FD) is the
number
of months (last year from the survey took place) that an household had
bought food-grains (minimum = 0 month, maximum = 12 months or whole year
deficit).
Even though I "jitter"-ed the minimum or maximum FD value only (eg.
FD=0+1e-6 or FD=12-1e-6), nothing changed to the result.

The formula I used is like this:
------------------------------**------------------------------**--
glm(FD ~ Fsize, data = subFS)
--
Coefficients:
(Intercept)        Fsize
     7.7913      -0.3092

Degrees of Freedom: 29 Total (i.e. Null);  28 Residual
Null Deviance:      463
Residual Deviance: 425.5        AIC: 170.7
------------------------------**------------------------------**--

I appreciate for any clarification.

Best wishes,
Wim

David Winsemius, MD
Heritage Laboratories
West Hartford, CT

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