Duncan's test with two-way ANOVA

[David Goda]

In our version 6 of SPSS for Windows, Duncan's multiple range test is a
standard option in one-way ANOVA (via "compare means"), but we cannot find
it for a more sophisticated ANOVA (via "ANOVA"). Are we missing something
obvious?
-----------------------------

David Goda
SCIT, Univ. of Wolverhampton
Wulfruna Street Phone (01902) 321444
Wolverhampton WV1 1SB Email d.g...@wlv.ac.uk

[Jodi Elliott]

I have run a logistic regression analysis and need to report the results
in table format. Looking at examples in the published literature, I see
that several people have reported b (clear enough), s.e. (also clear),
chi-square, df, and something called "Pseudo R^2." Each predictor has a
b and s.e. reported, along with "Unique Pseudo R^2," then there is a
"Pseudo R^2" at the bottom of the table, after the chi-square.

My SPSS output provides -2 LL for both constant-only model and for full
model, a Goodness of Fit value, Model Chi-Square along with df and significance
level, Improvement of full model over constant-only model, B, S.E., Wald,
df, Sig (of Wald statistic, I believe), R, and Exp(B) which I have heard
from this group is an odds ratio.

Can someone tell me what, if anything, in my output corresponds to this
"Pseudo R^2" that people seem to be reporting out? Do I need to specify
something in my syntax that I'm currently missing? Thanks in advance for
any help you can offer.

Jodi Callahan
Tulane University

[Markus Quandt]

In article <5j0c1h$dmm$1...@rs10.tcs.tulane.edu>, Jodi Elliott wrote:

>My SPSS output provides -2 LL for both constant-only model and for full
>model, a Goodness of Fit value, Model Chi-Square along with df and significance
>level, Improvement of full model over constant-only model, B, S.E., Wald,
>df, Sig (of Wald statistic, I believe), R, and Exp(B) which I have heard
>from this group is an odds ratio.
>
>Can someone tell me what, if anything, in my output corresponds to this
>"Pseudo R^2" that people seem to be reporting out? Do I need to specify

--
Jodi,

pseudo R^2 is NOT provided by any of the LOG REG switches, but you can
very easily calculate it by hand (i.e., a pocket calculator ;-) ).
Before I give instructions, let me mention that there are several
pseudo R^2 coefficients which all serve as a (rather poor) replacement
for the R^2 you have in linear regression. That is, they serve as a
tool to judge model fit on a standardized scale between 0 and 1. What
is most commonly used is 'McFadden's' pseudo R^2', which simply gives
the relative reduction of deviance that is produced by the
independent variables in your model, compared to a model with the
constant only.
SPSS gives you all the numbers you need to compute McFadden's R^2. The
first occurence of -2LL:

...
Beginning Block Number 0. Initial Log Likelihood Function

-2 Log Likelihood 952,60313

* Constant is included in the model.
...

is the baseline for the comparison of the relative gain by fitting
your model. Following the iteration history, you find the -2LL value
of your FITTED model:

...
Estimation terminated at iteration number 5 because
Log Likelihood decreased by less than ,01 percent.

-2 Log Likelihood 722,333
Goodness of Fit 668,275

...

Both -2LL values are measures of the extent to which the distribution
'predicted' by your models (the model with only the constant could
also be used to make predictions) deviates from the real distribution
found in your data. So their difference 952.60313 - 722.333 =
230.27013 is the gain you get by introducing your predictors. When
you look at the next block of output, you will notice that SPSS has
already calculated this value as 'Model Chi-Square':

...
Chi-Square df Significance

Model Chi-Square 230,270 24 ,0000
Improvement 230,270 24 ,0000

...

To standardize, you divide the difference by the baseline:
230.27/952.6 gives 0.242 as McFadden's pseudo R^2.

The second value, labelled 'Improvement' gives the reduction of -2LL
by the variables introduced in the current step of stepwise
procedures, which of course is the same as the model chi-square when
all variable were entered in one block, as I did here. But IF you run
stepwise regressions, be careful to choose the right value.

I don't know for sure what is being referred to by 'unique pseudo
R^2', as I haven't come across this term before, but would guess that
it means the increase in pseudo R^2 by a particular variable, given
all other independent variables are already present in the model. If
this guess is correct, it would be a sort of a partial contribution,
remotely comparable to BETA coefficients in OLS. To compute this
(this part is pure speculation, corrections welcome), you would run
multiple models (one for each independent variable) with the variable
of interest entered in a second step, all others being present then.
Now use the 'Improvement' value from the output for the second step
(which should be significant, of course) and divide by the initial
-2LL value, and there you are.

Regards, M. Quandt

---------------------------------------------------------------
Markus Quandt qua...@wiso.uni-koeln.de
Universitaet zu Koeln
University of Cologne, Germany

[David Nichols]

In article <F0/Uz4ANTI...@wiso-r610.wiso.uni-koeln.de>,

Just to clarify one thing: in releases prior to 7.5, we give two
-2 LL based chi^2 tests for parameters in the model: Model and
Improvement. Model compares the current model with the model at
the end of the previous block (which will only be the constant
only model if you use one block). Improvement compares the current
model to the one at the previous step, which will agree with the
Model value if a stepwise method is not used. If you fit multiple
blocks, you have to go back and refit it in one block or else
compute the real "model" value by hand.

In Release 7.5, you get three values: Model, Block and Step, so
you get whatever you need at any point.

--
-----------------------------------------------------------------------------
David Nichols Senior Support Statistician SPSS, Inc.
Phone: (312) 329-3684 Internet: nic...@spss.com Fax: (312) 329-3668
-----------------------------------------------------------------------------

[David Nichols]

In article <1.5.4.16.1997041...@wlv.ac.uk>,

Duncan's test was designed for the one way case. I know of no extension
of it to more complicated designs (actually, it was designed for the
more specific one way case with equal N). It actually doesn't work as
a multiple comparison procedure for controlling overall Type I error
even in the one way case (see, e.g., Jason Hsu's _Multiple Comparisons:
Theory and Methods_).

[David Nichols]

In article <5j0c1h$dmm$1...@rs10.tcs.tulane.edu>,

Jodi Elliott <jell...@rs1.tcs.tulane.edu> wrote:
>I have run a logistic regression analysis and need to report the results
>in table format. Looking at examples in the published literature, I see
>that several people have reported b (clear enough), s.e. (also clear),
>chi-square, df, and something called "Pseudo R^2." Each predictor has a
>b and s.e. reported, along with "Unique Pseudo R^2," then there is a
>"Pseudo R^2" at the bottom of the table, after the chi-square.
>

>My SPSS output provides -2 LL for both constant-only model and for full
>model, a Goodness of Fit value, Model Chi-Square along with df and significance
>level, Improvement of full model over constant-only model, B, S.E., Wald,
>df, Sig (of Wald statistic, I believe), R, and Exp(B) which I have heard
>from this group is an odds ratio.
>
>Can someone tell me what, if anything, in my output corresponds to this
>"Pseudo R^2" that people seem to be reporting out? Do I need to specify

>something in my syntax that I'm currently missing? Thanks in advance for
>any help you can offer.
>
>Jodi Callahan
>Tulane University

None of these things on the SPSS output is a pseudo-R^2. We added two
types of pseudo-R^2 measures for the entire model to Release 7.5. I
don't know what people are reporting for individual variables; I'd be
interested in seeing formulas for those.