?? psy6003 logistic regression and discriminant analysis.mht
字號:
takes the value 1 rise by a factor of ten, so they go from an even =
chance=20
(1:1) to 10:1, i.e. <I>p</I> changes to 0.909. If <I>x</I><SUB>1</SUB> =
further=20
increases to 2, then the odds will move to 100:1, a <I>p</I> value of =
0.990;=20
and so on. This leads to a convenient way of representing the results =
of=20
logistic regression by a plot showing the odds change produced by unit =
changes=20
in different independent variables. A good example is the figure in =
Johnson et=20
al's (1992) report on risk factors for contracting AIDS. </P>
<LI><B>Significance of individual regressors</B>=20
<P>SPSS prints out the value of what it calls the <B>Wald =
statistic</B> for=20
each regressor in each model, together with a corresponding =
significance=20
level. The Wald statistic has a chi-squared distribution, but apart =
from that=20
it is used in just the same way as the <I>t</I> values for individual=20
regressors in linear regression. However, the Wald test gives the =
wrong=20
results for very high coefficient values, and if you encounter those, =
you=20
should use the difference of -2<I>LL</I> values for models with and =
without=20
the predictor instead. </P>
<LI><B>A reassuring coda</B>=20
<P>Some parts of this section may have seemed rather complex, and you =
may be=20
tempted to give up on logistic regression at this point, deciding that =
you=20
will never understand it. Remember, though, that the quantitative=20
interpretation of the coefficients does not matter too much if all you =
want to=20
do is any or all of the following:</P>
<UL>
<LI>see how well you can classify people into groups from a =
knowledge of=20
independent variables; this is addressed by the classification table =
and the=20
<I>LRFC</I><SUB>1</SUB> goodness of fit statistics discussed above;=20
<LI>see whether the independent variables as a whole significantly =
affect=20
the dependent variable; this is addressed by the Model Chi-square =
statistic.=20
<LI>identify the best variables to use in prediction. This is more =
complex=20
than with linear regression, because SPSS does not give you =
<B>beta</B>=20
values directly in the logistic regression output. But you can if =
necessary=20
compare regressors by multiplying each coefficient by the standard =
deviation=20
of the corresponding variable. The results will not be beta values, =
but=20
their ranking will reflect relative importance of the regressors in =
the same=20
way as beta values do.=20
<LI>determine whether particular independent variables have =
significant=20
effects on the dependent variable; this can be done using the Wald=20
statistics which SPSS produces, or by comparing the -2<I>LL</I> =
values for=20
models with and without the variables concerned. =
</LI></UL></LI></UL>
<P><I>back to <A=20
href=3D"http://www.ex.ac.uk/~SEGLea/multvar2/disclogi.html#top">top</A></=
I></P>
<H3><A name=3Drefs></A>References and further reading</H3>
<UL>
<LI>SPSS Advanced Statistics manual, for versions 4 onwards.=20
<LI>Darlington, R. B. (1990), <I>Regression and linear models</I>. New =
York:=20
McGraw-Hill. Chapter 18.=20
<LI>Johnson, A. M., Wadsworth, K., Bradshaw, S., & Field, J. =
(1992).=20
Sexual lifestyles and HIV risk. <I>Nature</I>, <I>360</I>, 410-412.=20
<LI>Press, S. J., & Wilson, S. (1978). Choosing between logistic=20
regression and<B> </B>discriminant analysis. <I>Journal of the =
American=20
Statistical Association, 73</I>,<B> </B>699-705. This paper sets out =
to show=20
that logistic regression is better than discriminant analysis and ends =
up=20
showing that at a qualitative level they are likely to lead to the =
same=20
conclusions. But it is very useful for clarifying terms. </LI></UL>
<P><I>back to <A=20
href=3D"http://www.ex.ac.uk/~SEGLea/multvar2/disclogi.html#top">top</A></=
I></P>
<P>
<HR>
<P></P>
<H3><A name=3Dexamples></A>Examples </H3>
<OL>
<LI>The SPSS system file /singer1/eps/psybin/stats/atmmini.sys is a =
cut-down=20
version of a file obtained from the ESRC data archive in Essex. This =
file is=20
also available (in portable format) on the PSYCHO fileserver, =
currently in=20
directory \scratch\segl\stats. Copy the system file into your own file =
space.=20
<LI>The study examined the factors that influenced whether or not =
people had=20
cash cards and the original report consists of a long series of=20
cross-tabulations. But obviously the data are ideally suited to =
logistic=20
regression. The variables we have included are HAVECARD (the dependent =
variable) and age, sex, 10 attitude scales, judgements of how serious =
various=20
problems were (prob1 to prob10) income (inc) and problems in use =
(useprob1 to=20
useprob3). Carry out two logistic regressions, using first FSTEP and =
then=20
BSTEP.=20
<LI>Carry out a couple of discriminant analyses on these data (using =
different=20
methods). Compare the results with those of the logistic regression. =
</LI></OL>
<P>Remember not to take assumptions for granted. </P>
<P><I>back to <A=20
href=3D"http://www.ex.ac.uk/~SEGLea/multvar2/disclogi.html#top">top</A></=
I></P>
<P>
<HR width=3D"100%">
<A href=3D"http://www.exeter.ac.uk/~SEGLea/">Stephen Lea</A>=20
<HR>
<P></P>
<ADDRESS>University of Exeter</ADDRESS>
<ADDRESS>Department of Psychology<BR>Washington Singer =
Laboratories<BR>Exeter=20
EX4 4QG<BR>United Kingdom<BR>Tel +44 1392 264626<BR>Fax +44 1392 264623=20
</ADDRESS>
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<P><A href=3D"http://www.exeter.ac.uk/~PWebley">Send questions and =
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