Logistic Regression results advice

[Katina Dimoulias]

Hello members,

I am having a little trouble interpreting some of my logistic regression
results and would appreciate assistance explaining them.  I ran separate
binary logistic regressions with a set of 4 predictors (measured on a
5-point Likert scale)  and 9 outcome variables (categories:
occasionally/often).  I have 117 participants.

I am having trouble understanding:
1. Why some outcomes have Omnibus Tests of Model Coefficient results that
indicate a 'good fit' p.001 for the model, overall classification did not
improve, Nagelkerke R2 = .22, however none of the predictors are
significant, and
2. Why another outcome has Omnibus Tests of Model Coefficient results that
indicate there is not a 'good fit' p.100, however one of the predictors is
significant p.03.

Your advice would be much appreciated.

Thanks,
Katina

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[SR Millis-3]

In the case of #1, I suspect that you might have a high degree of collinearity among your covariates/predictor variables.  You'll need to examine your condition indexes and variance decomposition proportions in order to find the collinearity.

In #2, you probably have a misspecified model, ie, you've not included enough of the important covariates in your model.

Overall, you probably have too many covariates given your sample size. You need at least 6-10 events/subjects per covariate, ie, the sample size of the smaller of the 2 groups in the logistic regression context.

Scott R Millis, PhD, MEd, ABPP (CN,CL,RP), CStat
Professor & Director of Research
Dept of Physical Medicine & Rehabilitation
Wayne State University School of Medicine
261 Mack Blvd
Detroit, MI 48201
Email:  [hidden email]
Tel: [phone]
Fax: [phone]


--- On Tue, 1/20/09, Katina Dimoulias <[hidden email]> wrote:

> From: Katina Dimoulias <[hidden email]>
> Subject: Logistic Regression results advice
> To: [hidden email]
> Date: Tuesday, January 20, 2009, 7:51 AM
> Hello members,
>
> I am having a little trouble interpreting some of my
> logistic regression
> results and would appreciate assistance explaining them.  I
> ran separate
> binary logistic regressions with a set of 4 predictors
> (measured on a
> 5-point Likert scale)  and 9 outcome variables (categories:
> occasionally/often).  I have 117 participants.
>
> I am having trouble understanding:
> 1. Why some outcomes have Omnibus Tests of Model
> Coefficient results that
> indicate a 'good fit' p.001 for the model, overall
> classification did not
> improve, Nagelkerke R2 = .22, however none of the
> predictors are
> significant, and
> 2. Why another outcome has Omnibus Tests of Model
> Coefficient results that
> indicate there is not a 'good fit' p.100, however
> one of the predictors is
> significant p.03.
>
> Your advice would be much appreciated.
>
> Thanks,
> Katina
>
> =====================
> To manage your subscription to SPSSX-L, send a message to
> [hidden email] (not to SPSSX-L), with no body
> text except the
> command. To leave the list, send the command
> SIGNOFF SPSSX-L
> For a list of commands to manage subscriptions, send the
> command
> INFO REFCARD

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[Hector Maletta]

The significance of predictors refers to the chance that the true value of
the coefficient in the population is zero, and depends jointly on the
estimate for the coefficient and the size of the sample. On the other hand,
the goodness of fit is the capacity of the model to predict the individual
occurrence of the dependent event. It may well be that all coefficients are
significant but few events (or non-events) are correctly predicted. This may
be because the threshold for predicting the event is (by default) a
predicted probability greater than 0.5, and the model may not predict such a
large probability for people actually having the event. You may improve the
"fit" in such a situation by setting a lower threshold (for instance, if the
overall occurrence of the event is 10%, predict the event for all
individuals whose predicted probability in the equation is above 10%).
However, as explained below, this makes little sense in my humble opinion.
Something you may want to consider is that probabilities are best
interpreted in a frequentist or populational way, i.e. as referred to
populations or groups, and not to individuals. Each particular individual
has not a "probability" of suffering the event: she either suffers it or she
doesn't. The probability is the relative frequency of the event in a group
of people sharing certain values of the predictors. What the equation tells
you is that, for instance, the group of respondents who are males aged 30-44
with college education are 50% more likely to do it often than the group of
respondents who are females aged 15-29 without a college education (or
whatever is your "base" or "reference" group). The key word is "group". The
relative frequency of people responding "often" is expected to be higher in
one group relative to the other, but the particular outcome for a given
individual is strictly indeterminate, just as the outcome of a particular
coin throw is indeterminate: you only know that 50% of all throws will be
tails and 50% heads, but you do not know a thing about the next coin, except
that the chances of it falling and resting on its side (50% head and 50%
tails) are practically nil: any particular throw would be either 100% head
or 100% tail. Probabilities do not apply to individuals, but to groups. I
know there is a long tradition to the contrary, but it soon leads into
contradictions (you may want to read the book by Gerd Gigerenzer and
Reinhard Selten, Bounded Rationality, for a discussion on this issue).
Hector
-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of
Katina Dimoulias
Sent: 20 January 2009 10:51
To: [hidden email]
Subject: Logistic Regression results advice

Hello members,

I am having a little trouble interpreting some of my logistic regression
results and would appreciate assistance explaining them.  I ran separate
binary logistic regressions with a set of 4 predictors (measured on a
5-point Likert scale)  and 9 outcome variables (categories:
occasionally/often).  I have 117 participants.

I am having trouble understanding:
1. Why some outcomes have Omnibus Tests of Model Coefficient results that
indicate a 'good fit' p.001 for the model, overall classification did not
improve, Nagelkerke R2 = .22, however none of the predictors are
significant, and
2. Why another outcome has Omnibus Tests of Model Coefficient results that
indicate there is not a 'good fit' p.100, however one of the predictors is
significant p.03.

Your advice would be much appreciated.

Thanks,
Katina

=====================
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=====================
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