<UL>No. In discriminant analysis the groups (clusters) are determined=20
    beforehand and the object is to determine the linear combination of=20
    independent variables which best discriminates among the groups. In =
cluster=20
    analysis the groups (clusters) are not predetermined and in fact the =
object=20
    is to determine the best way in which cases may be clustered into =
groups.=20
</UL>
  <P><A name=3Dconstant></A></P>
  <LI><B>When does the discriminant function have no constant term?</B>=20
  <UL>When the data are standardized or are deviations from the mean. =
</UL>
  <P><A name=3Dhov></A></P>
  <LI><B>How important is it that the assumptions of homogeneity of =
variances=20
  and of multivariate normal distribution be met?</B>=20
  <UL>Lachenbruch (1975) indicates that DA is relatively robust even =
when=20
    there are modest violations of these assumptions. Klecka (1980) =
points out=20
    that dichotomous variables, which often violate multivariate =
normality, are=20
    not likely to affect conclusions based on DA. </UL>
  <P><A name=3Dbetas></A></P>
  <LI><B>In DA, how can you assess the relative importance of the =
discriminating=20
  variables?</B>=20
  <UL>The same as in regression, by comparing beta weights. If not =
output=20
    directly by one's statistical package (SPSS does), one may obtain =
beta=20
    weights by running DA on standardized scores. That is, betas are=20
    standardized discriminant function coefficients. The ratio of the =
betas is=20
    the relative contribution of each variable. Note that the betas will =
change=20
    if variables are added or deleted from the equation.=20
    <P><I>Dummy variables</I>. As in regression, dummy variables must be =

    assessed as a group, not on the basis of individual beta weights. =
This is=20
    done through <B>hierarchical discriminant analysis</B>, running the =
analysis=20
    first with, then without the set of dummies. The difference in the =
squared=20
    canonical correlation indicates the explanatory effect of the set of =

    dummies.=20
    <P>Alternatively, for interval independents, one can correlate the=20
    discriminant function scores with the independents. The =
discriminating=20
    variables which matter the most to a particular function will be =
correlated=20
    highest with the DA scores. </P></UL>
  <P><A name=3Dmle></A></P>
  <LI><B>What is the maximum likelihood estimation method in =
discriminant=20
  analysis (logistic discriminate function analysis)?</B>=20
  <UL>Using mle, a discriminant function is a function of the form T =3D =
k1X1 +=20
    k2X2 + ... + knXn, where X1...Xn are the differences between the two =
groups=20
    on the ith independent variable, k1...kn are the logit coefficients, =
and T=20
    is a function which classes the case into group 0 or group 1. If the =
data=20
    are unstandardized, there is also a constant term. The discriminant =
function=20
    arrives at coefficients which set the highest possible ratio of=20
    between-group to within-groups variance (similar to the ANOVA F =
test, except=20
    that in DA the group variable is the dependent rather than the =
independent).=20
    This method, called <B>logistic discriminate function analysis</B>, =
is=20
    supported by SPSS. </UL>
  <P><A name=3Dfisher></A></P>
  <LI><B>What are Fisher's linear discriminant functions? </B>
  <UL>The classical method of discriminant classification calculated one =
set=20
    of discriminant function coefficients for each dependent category, =
using=20
    these to make the classifications. SPSS still outputs these =
coefficients if=20
    you check the "Fisher's" box under the Statistics option in =
discriminant=20
    function analysis. </UL>
  <P><A name=3Dstep></A></P>
  <LI><B>What is stepwise DA?</B>=20
  <UL>Stepwise procedures select the most correlated independent first, =
remove=20
    the variance in the dependent, then select the second independent =
which most=20
    correlates with the remaining variance in the dependent, and so on =
until=20
    selection of an additional independent does not increase the =
R-squared (in=20
    DA, canonical R-squared) by a significant amount (usually =
signif=3D.05). As in=20
    multiple regression, there are both forward (adding variables) and =
backward=20
    (removing variables) stepwise versions.=20
    <P>In SPSS there are several available criteria for entering or =
removing new=20
    variables at each step: Wilks?lambda, unexplained variance,=20
    Mahalanobis?distance, smallest F ratio, and Rao=92s V. The =
researcher typically=20
    sets the critical significance level by setting the "F to remove" in =
most=20
    statistical packages.=20
    <P>Stepwise procedures are sometimes said to eliminate the problem =
of=20
    multicollinearity, but this is misleading. The stepwise procedure =
uses an=20
    intelligent criterion to set order, but it certainly does not =
eliminate the=20
    problem of multicollinearity. To the extent that independents are =
highly=20
    intercorrelated, the standard errors of their standardized =
discriminant=20
    coefficients will be inflated and it will be difficult to assess the =

    relative importance of the independent variables.=20
    <P>The researcher should keep in mind that the stepwise method =
capitalizes=20
    on chance associations and thus significance levels are worse (that =
is,=20
    numerically higher) than the true alpha significance rate reported. =
Thus a=20
    reported significance level of .05 may correspond to a true alpha =
rate of=20
    .10 or worse. </P></UL>
  <P><A name=3Dmancova></A></P>
  <LI><B>I have heard DA is related to MANCOVA. How so?</B>=20
  <UL>Discriminant analysis can be conceptualized as the inverse of =
MANCOVA.=20
    MANCOVA can be used to see the effect on multiple dependents of a =
single=20
    categorial independent, while DA can be used to see the effect on a=20
    categorical dependent of multiple interval independents. The SPSS =
MANOVA=20
    procedure, which also covers MANCOVA, can be used to generate =
discriminant=20
    functions as well, though in practical terms this is not the easiest =
route=20
    for the researcher interested in DA. </UL>
  <P></P></LI></UL>
<UL></UL>
<P><BR>
<H2>Bibliography</H2>
<UL>
  <LI>George H. Dunteman (1984). <I>Introduction to multivariate =
analysis</I>.=20
  Thousand Oaks, CA: Sage Publications. Chapter 5 covers classification=20
  procedures and discriminant analysis.=20
  <P></P>
  <LI>Klecka, William R. (1980). <I>Discriminant Analysis</I>. =
Quantitative=20
  Applications in the Social Sciences Series, No. 19. Thousand Oaks, CA: =
Sage=20
  Publications.=20
  <P>Lachenbruch, P. A. (1975). <I>Discriminant Analysis</I>. NY: =
Hafner.=20
  <P></P>
  <LI>Press, S. J. and S. Wilson (1978). Choosing between logistic =
regression=20
  and discriminant analysis. <I>Journal of the American Statistical=20
  Association</I>, Vol. 73: 699-705. The authors make the case for the=20
  superiority of logistic regression for situations where the =
assumptions of=20
  multivariate normality are not met (ex., when dummy variables are =
used),=20
  though discriminant analysis is held to be better when assumptions are =
met.=20
  They conclude that logistic and discriminant analyses will usually =
yield the=20
  same conclusions, except in the case when there are independents which =
result=20
  in predictions very close to 0 and 1 in logistic analysis. </LI></UL>
<P>
<P>
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