Re: Probit analysis

On Wed, 17 Sep 2008 10:52:25 -0700 (PDT), ark561@xxxxxxxxx wrote:

On Sep 16, 7:52 pm, RichUlrich <rich.ulr...@xxxxxxxxxxx> wrote:
On Tue, 16 Sep 2008 14:12:02 -0700 (PDT), ark...@xxxxxxxxx wrote:
On Sep 16, 4:47 pm, Paul Rubin <ru...@xxxxxxx> wrote:
ark...@xxxxxxxxx wrote:
Hello,

I am attempting to model binomial categorical data using a probit
model. I only have one explanatory variable in this model. The issue
that I am running into is that for some experiments I am observing a
non-increasing rate of proportion of a success. In other words, the
proportion of a success increases up until a particular value of the
explanatory variable, and then the proportion of successes decreases
for larger values of the explanatory variable.

This does not always occur, but when it does, is there another method
that can be used to model the data apart from a probit/logit model?

You can stick with a probit or logit model but use a quadratic rather
than linear expression. Just throw in the square of the original
predictor as another variable. If the marginal increase and marginal
decrease in the (logged) odds ratios are not symmetric, you might need
to go higher than quadratic.

As a second question, suppose that I have two probit models, is there
a general test that can be used to determine whether or not one model
is significantly different from another?

You're talking about the same model (same functional form, same
predictor(s)) fitted on two different samples?

/Paul

Hi Paul,

Thank you for your response.

Yes, I am examining the same model on two different samples where
something changed from one samples to the other. For example, the
method in which the individual items of the samples are constructed,
or the temperature at which they are kept.

A conventional way to perform such a statistical test is to
fit one parameter (or set) to the combined data, and then
test whether an additional parameter (or set) reduces the
error in fit by a "statistically significant" amount.

In regression with one predictor and 2 groups, the two
parameters for a new group are the slope and the intercept.

The difference between groups is usually a test on a
difference in intercept, whereas a difference in slope is
problematic (usually, a violation of an assumption).

--
Rich Ulrich

Hi Rich,

This is something that I tried, but I may be mistaken on what the
results should be.

I gathered data at the same levels of the explanatory variables for
two different samples that was an indicator variable. The variable
ended up being statistically significant at the 0.05 level (the p-
value was above 0.9),

Is this an inadvertant error, or are you all messed up?

"Statistically significant" is indicated by p LESS THAN 0.05,
or some such. Not, P-value above 0.9.


but the confusion I have is that the model is
different than the models for each of the groups when they are fit
separately.

Here is a simple example of "extra parameter."
Let's say that the heights of a sample of
young males, some age, average 1.40 meters, and for a sample of
females, same age, same N, average 1.50 m.

Now, the results can be written separately, as I just did. More
briefly, M=140, F=150.
Or, we can write,
Height= 1.45 + 0.05*Sex where sex is encoded -1/+1 for
Male, Female.

No information is lost by including the two results in one equation.
It would be possible to test whether the "0.05" is "different from
zero" for these two samples when tested against the internal
variation.

The regression model that is created for two samples is
entirely similar, in the respect that it includes and encodes
the two original results. It is trickier to figure when the Ns are
not equal, but the combined equation shows both results.


I guess my disconnection is that I have it in my mind that the
probability of a success occurring at a particular value of the
explanatory variable should be the same whether I fit the model to a
set of data by itself or if I fit the model to data that consists of
data from two different samples that includes an indicator variable
that declares which sample we are examining.

And, if the slopes are not forced to be equal, a dummy for slopes.
Did you omit that?

Intuitively, I understand that the models will be different, since I
am fitting a model to a different (combined) data set, however I'm
having difficulty accepting the fact that the probability of a success
changes when adding data from another sample.

Does this make sense?
No.

I don't have any confidence that you know how to read your
regression results, so you might have to be a lot more
specific about showing your results if you want to ask some more.

--
Rich Ulrich
.

Relevant Pages

  • Re: Probit analysis
    ... non-increasing rate of proportion of a success. ... error in fit by a "statistically significant" amount. ... I gathered data at the same levels of the explanatory variables for ...
    (sci.stat.math)
  • Re: Probit analysis
    ... non-increasing rate of proportion of a success. ... error in fit by a "statistically significant" amount. ... parameters for a new group are the slope and the intercept. ...
    (sci.stat.math)