logistic regression 1st lecture.mht

这是博弈论算法全集第六部分:局面描述,其它算法将陆续推出.以便与大家共享

two=20
    independent variables when<BR>&gt;both (and possibly other variables =
as=20
    well) are in the model, such as<BR>&gt;incremental R square in =
linear=20
    regression.<BR><BR>For effect sizes I understand that the odds-ratio =
is the=20
    measure of choice.<BR>I don't know, however, how to determine an =
appropriate=20
    comparison of<BR>odds-ratios for two continuous predictors on =
different=20
    scales. <BR><BR>Another possibility would be to look at the change =
in model=20
    deviance<BR>attributed to both variables. <BR><BR>Another would be =
to=20
    calculate something called the structure coefficient.<BR>To do this, =
I think=20
    one calculates the predicted values for the outcome<BR>(predicted=20
    probabilities in this case), and correlating these=20
    predicted<BR>probabilities with each independent variable. Those =
with the=20
    strongest<BR>correlations would be the ones contributing most to the =
model.=20
    <BR><BR>I'm not an expert on this topic, so I welcome anyone willing =
to=20
    offer<BR>corrections to my comments; I'd like to better understand =
issues.=20
    =
<BR>___________________________________________________________________<B=
R>Bryan=20
    W. Griffin<BR>Phone: [phone]<BR>E-Mail: =
[e-mail]<BR>WWW:=20
    =
http://www2.gasou.edu/edufound/bwgriffin/<BR><BR>************************=
*********************</P><SPAN=20
    class=3DEUDORAHEADER>
    <P>From: Darran Caputo &lt;[e-mail]&gt; <BR></SPAN></P>
    <P>In response to (1).</P>
    <P>- I find the most straightforward way to understand the =
explanatory power=20
    of you model is a confusion matrix.</P>
    <P>- A confusion matrix is a 2-by-2 of Actual and Predicted values =
of the=20
    outcome under study.</P>
    <P>- A confusion matrix is a function of the CUTOFF chosen to =
classify=20
    observations.</P>
    <P>-The question is: How well does the classifier perform for a =
given=20
    CUTOFF.</P>
    <P>- Once you choose a given CUTOFF your confusion matrix is =
determined.</P>
    <P>- This leads to many interesting statistics:</P>
    <P>a. Sensitivity&nbsp; =3D (#actual positive and predicted =
positive)/(#=20
    actual positives) ~ P(PP|AP)</P>
    <P>b. Specificity =3D&nbsp; (#actual positive and predicted =
positive)/(=20
    #predicited positives) ~ P(AP|PP)</P>
    <P><BR>The next step is to plot Sensitivity on the vertical axis and =

    1-Specificity on the horizontal axis for cutoffs (predicted =
probabilities=20
    between 0 and 1). This curver is called a Receiver Operator Curve=20
    (ROC).&nbsp; The area under the curve is equivalent to the =
C-statistic=20
    reported in SAS Proc Logistic.&nbsp; The C-statistic ranges from .5 =
to 1=20
    where C=3D1 for a perfect model and C=3D.5 for a model no better =
than random=20
    classification.</P>
    <P>***********************</P>
    <P>A better analogy of R2 is Nagelkerke's R2 (many other authors =
also had a=20
    hand in this).&nbsp; It is 1 - exp(-LR/n) where LR is the likelihood =
ratio=20
    chi-square for the whole model and n is the number of observations =
(not the=20
    number of "events").</P>
    <P>See</P>
    <P>@article{nag91not,&nbsp;&nbsp; author =3D {Nagelkerke, N. J.=20
    D.},&nbsp;&nbsp; journal =3D {Biometrika},&nbsp;&nbsp; pages =3D=20
    {691-692},&nbsp;&nbsp; title =3D {A note on a general definition of =
the=20
    coefficient of determination},&nbsp;&nbsp; volume =3D =
{78},&nbsp;&nbsp; year =3D=20
    {1991},&nbsp;&nbsp; annote =3D {predictive accuracy; maximum =
likelihood</P>
    <P>The index used by SPSS is a mixture of two different types of=20
    chi-squares. Even if it only used LR chi-squares (partial LR and =
total LR),=20
    there is a problem.</P>
    <P>See&nbsp; @article{sch90,&nbsp;&nbsp; author =3D "Schemper,=20
    M.",&nbsp;&nbsp; journal =3D BKA,&nbsp;&nbsp; pages =3D =
"216-218",&nbsp;&nbsp;=20
    title =3D "The explained variation in proportional hazards =
regression=20
    (correction in 81:631, 1994)",&nbsp;&nbsp; volume =3D =
"77",&nbsp;&nbsp; year =3D=20
    "1990"</P>
    <P>and&nbsp; @article{sch92fur,&nbsp;&nbsp; author =3D "Schemper,=20
    M.",&nbsp;&nbsp; journal =3D BKA,&nbsp;&nbsp; pages =3D =
"202-204",&nbsp;&nbsp;=20
    title =3D "Further results on the explained variation in&nbsp;&nbsp; =

    proportional hazards regression",&nbsp;&nbsp; volume =3D =
"79",&nbsp;&nbsp;=20
    year =3D "1992"</P>
    <P>(BKA =3D Biometrika)</P>
    =
<P>----------------------------------------------------------------------=
------</P>
    <P>Frank E Harrell Jr<BR>Professor of Biostatistics and=20
    Statistics<BR>Division of Biostatistics and =
Epidemiology<BR>Department of=20
    Health Evaluation Sciences<BR>University of Virginia School of=20
    Medicine<BR>hesweb1.med.virginia.edu/biostatistics.html</P>
    <P><BR></P>
    <P><BR><BR><BR></P>
    <P><BR></P></BLOCKQUOTE>
  <P>&nbsp;</P></BLOCKQUOTE>
<P>Last revised: <!--webbot bot=3D"Timestamp" S-Type=3D"EDITED" =
S-Format=3D"%m/%d/%y" startspan -->05/22/00<!--webbot bot=3D"Timestamp" =
endspan i-checksum=3D"12262" -->=20
</P></BODY></HTML>

------=_NextPart_000_001C_01C00ACA.318D76C0
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://hobbes.uvm.edu/gradstat/psych341/header.gif
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------=_NextPart_000_001C_01C00ACA.318D76C0
Content-Type: image/gif
Content-Transfer-Encoding: base64
Content-Location: http://hobbes.uvm.edu/gradstat/psych341/lectures/Logistic%20Regression/Image195.gif
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