<HTML><HEAD><TITLE>R: Nonlinear Ordinal Regression Models</TITLE>
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<TABLE WIDTH="100%"><TR><TD>nordr {gnlm}</TD><TD ALIGN="right">R Documentation</TD></TR></TABLE>
<h2>Nonlinear Ordinal Regression Models</h2>
<h3>Description</h3>
<p>
<CODE>nordr</CODE> fits arbitrary nonlinear regression functions (with
logistic link) to ordinal response data by proportional odds,
continuation ratio, or adjacent categories.
<P>
Nonlinear regression models can be supplied as formulae where
parameters are unknowns in which case factor variables cannot be used
and parameters must be scalars. (See <CODE><A HREF="../../rmutil/html/finterp.html">finterp</A></CODE>.)
<P>
The printed output includes the -log likelihood (not the deviance),
the corresponding AIC, the maximum likelihood estimates, standard
errors, and correlations.
<h3>Usage</h3>
<PRE>
nordr(y, distribution="proportional", mu, linear=NULL, pmu,
pintercept, weights=NULL, envir=sys.frame(sys.parent()),
print.level=0, ndigit=10, gradtol=0.00001,
steptol=0.00001, fscale=1, iterlim=100, typsiz=abs(p),
stepmax=10*sqrt(p%*%p))
</PRE>
<h3>Arguments</h3>
<TABLE>
<TR VALIGN="TOP"><TD><CODE>y</CODE></TD>
<TD>
A vector of ordinal responses, integers numbered from zero to
one less than the number of categories or an object of class,
<CODE>response</CODE> (created by <CODE><A HREF="../../rmutil/html/restovec.html">restovec</A></CODE>) or <CODE>repeated</CODE>
(created by <CODE><A HREF="../../rmutil/html/rmna.html">rmna</A></CODE>) or <CODE><A HREF="../../rmutil/html/lvna.html">lvna</A></CODE>). If the
<CODE>repeated</CODE> data object contains more than one response variable,
give that object in <CODE>envir</CODE> and give the name of the response
variable to be used here.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>distribution</CODE></TD>
<TD>
The ordinal distribution: proportional odds,
continuation ratio, or adjacent categories.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>mu</CODE></TD>
<TD>
User-specified function of <CODE>pmu</CODE>, and possibly <CODE>linear</CODE>,
giving the logistic regression equation. This must contain the first
intercept. It may contain a linear part as the second argument to the
function. It may also be a formula beginning with ~, specifying a
logistic regression function for the location parameter, either a
linear one using the Wilkinson and Rogers notation or a general
function with named unknown parameters. If none is supplied, the
location is taken to be constant unless the linear argument is given.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>linear</CODE></TD>
<TD>
A formula beginning with ~ in W&R notation, specifying
the linear part of the logistic regression function.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>pmu</CODE></TD>
<TD>
Vector of initial estimates for the regression parameters,
including the first intercept. If <CODE>mu</CODE> is a formula with unknown
parameters, their estimates must be supplied either in their order of
appearance in the expression or in a named list.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>pintercept</CODE></TD>
<TD>
Vector of initial estimates for the contrasts with
the first intercept parameter (difference in intercept for successive
categories): two less than the number of different ordinal values.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>weights</CODE></TD>
<TD>
Weight vector for use with contingency tables.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>envir</CODE></TD>
<TD>
Environment in which model formulae are to be
interpreted or a data object of class, <CODE>repeated</CODE>, <CODE>tccov</CODE>,
or <CODE>tvcov</CODE>; the name of the response variable should be given in
<CODE>y</CODE>. If <CODE>y</CODE> has class <CODE>repeated</CODE>, it is used as
the environment.</TD></TR>
<TR VALIGN="TOP"><TD><CODE>others</CODE></TD>
<TD>
Arguments controlling <CODE><A HREF="../../base/html/nlm.html">nlm</A></CODE>.</TD></TR>
</TABLE>
<P>
</P>
<h3>Value</h3>
<P>
A list of class nordr is returned that contains all of the
relevant information calculated, including error codes.</P>
<h3>Author(s)</h3>
<p>
J.K. Lindsey
<h3>See Also</h3>
<p>
<CODE><A HREF="../../rmutil/html/finterp.html">finterp</A></CODE>, <CODE><A HREF="../../gnlm/html/fmr.html">fmr</A></CODE>, <CODE><A HREF="../../base/html/glm.html">glm</A></CODE>,
<CODE>glmm</CODE>, <CODE>gnlmm</CODE>, <CODE><A HREF="../../gnlm/html/gnlr.html">gnlr</A></CODE>,
<CODE><A HREF="../../gnlm/html/gnlr3.html">gnlr3</A></CODE>, <CODE><A HREF="../../gnlm/html/nlr.html">nlr</A></CODE>, <CODE><A HREF="../../gnlm/html/ordglm.html">ordglm</A></CODE>
<h3>Examples</h3>
<PRE>
# McCullagh (1980) JRSS B42, 109-142
# tonsil size: 2x3 contingency table
y <- c(0:2,0:2)
carrier <- c(rep(0,3),rep(1,3))
carrierf <- gl(2,3,6)
wt <- c(19,29,24,
497,560,269)
pmu <- c(-1,0.5)
mu <- function(p) c(rep(p[1],3),rep(p[1]+p[2],3))
# proportional odds
# with mean function
nordr(y, dist="prop", mu=mu, pmu=pmu, weights=wt, pintercept=1.5)
# using Wilkinson and Rogers notation
nordr(y, dist="prop", mu=~carrierf, pmu=pmu, weights=wt, pintercept=1.5)
# using formula with unknowns
nordr(y, dist="prop", mu=~b0+b1*carrier, pmu=pmu, weights=wt, pintercept=1.5)
# continuation ratio
nordr(y, dist="cont", mu=mu, pmu=pmu, weights=wt, pintercept=1.5)
# adjacent categories
nordr(y, dist="adj", mu=~carrierf, pmu=pmu, weights=wt,
pintercept=1.5)
#
# Haberman (1974) Biometrics 30, 589-600
# institutionalized schizophrenics: 3x3 contingency table
y <- rep(0:2,3)
fr <- c(43,6,9,
16,11,18,
3,10,16)
length <- gl(3,3)
# fit continuation ratio model with nordr and as a logistic model
nordr(y, mu=~length, weights=fr, pmu=c(0,-1.4,-2.3), pint=0.13,
dist="cont")
# logistic regression with reconstructed table
frcr <- cbind(c(43,16,3,49,27,13),c(6,11,10,9,18,16))
lengthord <- gl(3,1,6)
block <- gl(2,3)
summary(glm(frcr~lengthord+block,fam=binomial))
# note that AICs and deviances are different
</PRE>
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