{smcl}
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help for {cmd:reclass} {right: {browse "mailto:John_Hendrickx@yahoo.com":John Hendrickx}}
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{title:reclass}

{p 8 27}
{cmd:reclass} {it:varname} , {cmd:[}
  {cmdab:p:cnttab(}{it:string}{cmd:)}
  {cmdab:ad:just}
  {cmdab:b:estmod}
  {cmd:q(}{it:real}{cmd:)}
  {cmd:u(}{it:real}{cmd:)}
  {cmdab:d:ist(}{it:real}{cmd:)}
  {cmdab:as:soc(}{it:string}{cmd:)}
  {cmdab:m:isclass(}{it:real}{cmd:)}
  {cmdab:f:ormat(}{it:string}{cmd:)}
  {cmdab:v:erbose}
  {cmd:]}

{title:Description}

{p}
{cmd:reclass} is called by {help perturb} to create a table of
reclassification probabilities for use a perturbation analysis. It can
be used separately to experiment with different association patterns.
{it:varname} should refer to a categorical variable. {cmd:reclass}
creates a table of reclassification probabilities such that the
expected frequencies of the reclassified variable will be equal to the
frequency distribution of {it:varname}. In addition, an appropriate
association is imposed between the reclassified variable and
{it:varname}.

{title:Options}

{p 0 4}
{cmd:pcnttab} can be either a single value, a row or column matrix, or
a square matrix. Usually, a single value between 0 and 100 will be
specified indicating the percentage cases to be reclassified to the
same category.

{p 4 4}
If a row or column matrix is specified its dimensions must correspond
with the number of categories of {it:varname}. Values should be
between 0 and 100 and indicate the percentage of cases to be
reclassified to the same category for each category separately.

{p 4 4}
If a square matrix is specified, its dimensions must correspond with
the number of categories of {it:varname}. The matrix should indicate
the reclassification probabilities with the original variable in the
rows and the reclassified variables in the columns. Either percentages
or probabilities may be used. It is not necessary for these to add to
100 or to 1 respectively as {cmd:reclass} transforms them into
columnwise proportions.

{p}
In most cases, the {cmd:pcnttab} option will suffice. The options
below are useful for users familiar with loglinear models for square
tables (mobility models).

{p 0 4}
{cmd:adjust} By default, {cmd:reclass} defines reclassification
probabilities such that the expected frequencies of the reclassified
variable are the same as those of {it:varname} when the {cmd:pcnttab}
option is used. Use {cmd:noadjust} to suppress this and use the
percentages specified in the {cmd:pcnttab} option unmodified.
{cmd:noadjust} implies {cmd:nobestmod}.

{p 0 4}
{cmd:bestmod} By default, {cmd:reclass} imposes an appropriate pattern
of association between {it:varname} and its reclassified counterpart
when the {cmd:pcnttab} option is used. Use {cmd:nobestmod} to avoid
this. The reclassification probabilities will be adjusted to make the
expected frequencies of the reclassified variable equal to those of
{it:varname} but they will otherwise be close approximations of the
values specified in the {cmd:pcnttab} option.

{p 0 4}
{cmd:misclass} Maintained for compatiblity with the original version
of {cmd:misclass} and {help perturb}. Translated by {cmd:reclass} into
{cmd:pcnttab(100-}{it:misclass}{cmd:) noadjust}.

{p}
The options below can be used to specify the parameters of a pattern
of association. They will be ignored if {cmd:pncttab} was specified.

{p 0 4}
{cmd:q} the multiplicative parameter of a quasi-independence (constrained) model.

{p 0 4}
{cmd:u} the multiplicative parameter of a uniform association model.

{p 0 4}
{cmd:dist} the multiplicative parameter of a distance model.

{p 0 4}
{cmd:assoc} This allows users familiar with loglinear mobility models
to specify an association pattern of their own choice. The argument
for assoc should refer to a Stata program in which the variable
{cmd:paras} is defined as a function of the row variable {cmd:orig}
and the column variable {cmd:dest} to produce a loglinear pattern of
associaton.

{p 0 4}
{cmd:format }Specify a valid format for printing results. The default is %8.3f.

{p 0 4}
{cmd:verbose} debugging information.

{title:Remarks}

{p}
The basic idea of reclassifying cases in a perturbation analysis is
that each case will have a high probability, say 95%, of being
reclassified into the same category. The remaining cases could then be
distributed evenly among the remaining categories. There are two
problems with this approach. First, smaller categories will tend to
grow and larger categories will shrink after reclassification. Second,
the association between the original and the reclassified variable
will be arbitrary, with some reclassification categories being more
likely than others. Both problems occur more strongly to the extent
that the variable in question is unevenly distributed.

{p}
{cmd:reclass} solves thes problems by creating an initial table of
expected frequencies for the original by the reclassified variable,
given the initial reclassification probabilities as specified by the
{cmd:pcnttab} option. The parameters for an {it:appropriate} pattern
of association between the original and the reclassified variable are
derived from this table. Then an adjusted table of expected
frequencies is created with the pattern of a association found, such
that the expected frequency distribution of the reclassified variable
is identical to that of the original.

{p}
When a single percentage is specified in {cmd:pcnttab}, this
percentage is used for the diagonal cells of the initial
reclassification probabilities, with the remaining percentages
distributed evenly among the other categories. The {it:appropriate}
pattern of association in this case is a "quasi-independence
(constrained)" loglinear mobility model (Hout 1983, Goodman 1984).
The QI-C model makes the odds of reclassification to the
same/different category the same for all categories. In addition, the
reclassified category is independent of the original category, given
that they are not the same. This model is fitted to the intital table
of expected frequencies and a single {cmd:ln(q)} parameter is
reported. This {cmd:ln(q)} parameter is used to create the adjusted
table.

{p}
If the argument to {cmd:pcnttab} consists of a row or column vector of
percentages, {cmd:reclass} assumes uses different odds for
reclassification to the same versus different categories for each
category. The {cmd:pcnttab} argument forms the diagonal of the initial
reclassification percentages, the remaining percentages are
distributed evenly among the other categories. A quasi-independence
model is fitted to the initial table of expected frequencies, with
separate odds per category for reclassification to the same versus a
different category. An {cmd:ln(q)} parameter is reported for each
category of {it:varname}. These parameters are then used to create the
adjusted table.

{p}
If the argument to {cmd:pncttab} consists of a square matrix of
percentages, {cmd:reclass} assumes that {it:varname} is an ordered
categorical variable. Consequently, the percentages should be
constructed so that short distance reclassification is more likely
than long distance reclassification. {cmd:reclass} fits two models to
the intial table of expected frequencies, a "quasi-distance" model and
a "quasi-uniform association" model.

{p}
Both make short distance reclassification more likely than long
distance but this is even more pronounced for a quasi-uniform
association model than for a quasi-distance model. A quasi-distance
model makes the likelihood of reclassification proportionately lower
for each step away from the main diagonal. A quasi-uniform model on
the other hand is equivalent to a squared distance model,
reclassification is proportionately less likely for the squared number
of steps from the main diagonal.

{p}
Both models include an {cmd:ln(q)} parameter that increases the
likelihood of reclassification to the same category without affecting
short or long distance reclassification. The quasi-uniform model also
reports an {cmd:ln(u)} parameter, quasi-distance reports an
{cmd:ln(dist)} parameter. The best fitting model is chosen by
{cmd:reclass} and the deviance and df are reported.

{p}
If the patterns of associatioh used by {cmd:reclass} are not in fact
appropriate to the problem at hand, the {cmd:nobestmod} option could
be used. The final reclassification percentages will the be as close
as possible to those in the {cmd:pcnttab} option. The reclassification
probabilities will be adjusted to make the expected frequencies of the
reclassified variable equal to those of the original, leading to some
discrepancies.

{p}
Alternatively, {cmd:reclass} could be run using the {cmd:noadjust}
option. The returned result {cmd:e(gentab)} is then equal to the
initial table of expected frequencies. {cmd:e(gentab)} could be used
in a loglinear analysis to derive an appropriate model of association,
which could then be specified in the {cmd:assoc} option.

{p}
The adjusted table is created using a loglinear model of equal main
effects (a halfway model) and the appropriate pattern of association
as an offset variable. This is fitted to an arbitrary table with the
frequency distribution of {it:varname} as both its row and column
marginals. The predicted frequencies of this model form a symmetric
table with the pre-specified marginals and pattern of association
(Hendrickx, 2004; Kaufman & Schervish, 1986).

{p}
If the {cmd:q}, {cmd:u}, or {cmd:dist} parameters are known, these can
be specified directly in the corresponding options. For other patterns
of association, the {cmd:assoc} option could be used. {cmd:assoc}
should refer to a small program that defines the variable {cmd:paras}
in terms of {cmd:orig} and {cmd:dest} to produce a loglinear pattern
of association. For example:

{input:program define q25u5}
{input:    gen paras=(orig==dest)*ln(25) + orig*dest*ln(5)}
{input:end}

{p}
The command {cmd:reclass }{it:myvar}{cmd:, assoc(q25u5)} will produce
reclassification probabilities for the variable {it:myvar} using the
program q25u5. This is equivalent to using the options {cmd:q(25)} and
{cmd:u(5)}. Other loglinear mobility models can be defined in a
similar fashion.

{title:Saved results}

{p 0 4}
{cmd:r(gentab)}
{break}the initial expected table for the original by reclassified
variable

{p 0 4}
{cmd:r(margin)}
{break}the frequency distribution of {it:varname}

{p 0 4}
{cmd:r(classprob)}
{break}the cumulative reclassification probabilities. These will be
used by {help perturb} to randomly reclassify {it:varname}.

{title:References}

{p 0 4}
Goodman, Leo A. (1984).
{it:The analysis of cross-classified data having ordered categories}.
Cambridge, Mass.: Harvard University Press.

{p 0 4}
Hendrickx, J. (2004). Using standardised tables for interpreting
loglinear models. Submitted to {it:Quality & Quantity}.

{p 0 4}
Hout, M. (1983). {it:Mobility tables}. Beverly Hills: Sage Publications.

{p 0 4}
Kaufman, R.L., & Schervish, P.G. (1986). Using adjusted
crosstabulations to interpret log-linear relationships.
{it:American Sociological Review} 51:717-733

{p 0 4}
{browse "http://www.xs4all.nl/~jhckx/perturb/":http://www.xs4all.nl/~jhckx/perturb/}

{p}
Direct comments to: {browse "mailto:John_Hendrickx@yahoo.com":John Hendrickx}

{p}
{cmd:reclass} is available at
{browse "http://ideas.uqam.ca/ideas/data/bocbocode.html":SSC-IDEAS}.
Use {help ssc} {cmd:install perturb} to obtain the latest version.

{title:Also see}
{p 0 21}
On-line: help for
  {help vif}, {help collin}, {help coldiag}, {help coldiag2},
  {help perturb}
{p_end}