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predtable([keyword phrases] [,silent:T]) or predtable(Term [,keyword
  phrases] [,silent:T]), Term a CHARACTER scalar of the form "A.B. ...",
  where A, B are factors in current GLM model, or term:k, where k is a
  positive integer, and allowed keyword phrases seest:T, sepred:T,
  estimate:F, wtdmeans:T or x:values as for glmtable().

Keywords: glm, anova
predtable() computes a table of fitted values (estimated cell expected
values) based on the computations of the most recent GLM (generalized
linear or linear model) command such as anova() or poisson().  The table
has a dimension for each factor in the model, in the order the variables
appear in the model.  It is an error if there are no factors in the
model. See glmtable() for a somewhat more general function.

predtable(seest:T) does the same, except the result is a structure with
two components, 'estimate' and 'SEest' containing the table of fitted
values and their standard errors.

predtable(sepred:T) does the same, except the structure result has
components 'estimate' and 'SEpred', where SEpred contains standard
errors of prediction (usually sqrt(SEest^2 + MSE)) for each cell.

You can use both 'sepred:T' and 'seest:T' together, and can suppress the
table of estimates with 'estimate:F'.

predtable(Term) returns an estimated table of marginal means where the
margins are specified by Term.

Term must be a quoted string or CHARACTER scalar of the form
"Name1.Name2.Name3....", where Name1, Name2, ... are names of factors in
the current GLM model.

When there are k factor names in Term, the value of predtable() is an
array with k dimensions (vector if k = 1, matrix if k = 2), with the
dimensions ordered in the same order as in Term, not the order they
appear in the model if that is different.

predtable(Term, seest:T) does the same, but the result is a structure
with components 'estimate' and 'SEest', where SEest contains the
standard errors of the estimated marginal means.

You cannot use 'sepred:T' with Term when Term specifies a marginal
table, that is, Term does not include all factors in the model.

predtable(term:k [,seest:T]) is essentially equivalent to
predtable(TERMNAMES[k] [,seest:T]), computing the marginal table
matching term k in the model.

You cannot use predtable(Term [,...]) after anova() with a balanced
design unless Term includes all the factors in the model.

  Cmd> anova("y=a+b") # two-way ANOVA
  Model used is y=a+b
  WARNING: summaries are sequential
                  DF          SS          MS
  CONSTANT         1    0.021986    0.021986
  a                2      12.082       6.041
  b                3      12.419      4.1397
  ERROR1          24      39.977      1.6657

  Cmd> predtable() # estimates of cell means
  (1,1)      1.0316     0.23603    -0.43016     -1.3688
  (2,1)     0.98354     0.18795    -0.47824     -1.4169
  (3,1)      2.1081      1.3125     0.64631    -0.29238

  Cmd> predtable(seest:T,sepred:T) #cell mean estimates and SE's
  component: estimate
  (1,1)      1.0316     0.23603    -0.43016     -1.3688
  (2,1)     0.98354     0.18795    -0.47824     -1.4169
  (3,1)      2.1081      1.3125     0.64631    -0.29238
  component: SEest           [SE of estimated cell mean]
  (1,1)      1.2906     0.48563     0.58437     0.57713
  (2,1)      1.4245     0.57943      0.4888     0.57981
  (3,1)      1.4247      0.4894     0.56226     0.66824
  component: SEpred          [SE of prediction for cell]
  (1,1)      1.8252       1.379      1.4168      1.4138
  (2,1)      1.9222      1.4147      1.3801      1.4149
  (3,1)      1.9223      1.3803      1.4078      1.4534

  Cmd> predtable(a,seest:T) # marginal mean estimate and SE's
  component: estimate
  (1)    -0.13284    -0.18092     0.94363
  component: SEest
  (1)     0.44971      0.5415     0.56229

  Cmd> predtable(term:2) #second term is a
  (1)    -0.13284    -0.18092     0.94363

predtable(silent:T) and predtable(Term, silent:T) do the same, except
that certain advisory messages are suppressed.  'silent:T' can be used
with any other keywords.  The default value of 'silent' is False unless
the value of option' 'warnings' is False.

             Behavior when there are variates in the model
The fitted values are by default computed with each variate set to its
unweighted mean value and thus are what are sometimes called the
covariate adjusted cell means.

predtable(wtdmeans:T [,...]) does the same except it adjusts cell fitted
values to the weighted means of the variates.  You can use wtdmeans:T
only when there are variates and when the previous GLM command used
weighted OLS (anova() or manova()).  This option would be probably
appropriate when the weights were proportional to sample sizes.

predtable(x:Vals [,...]), where Vals is a REAL vector with length = the
number of variates (non-factors) in the model, does the same
computation, except it uses the elements of Vals instead of unweighted
or weighted variate means.  This option allows you to estimate cell
means that are adjusted to any level of the covariates.  Use of x:Vals
is an error if there are no variates in the current GLM model.

predtable() and predtable(Term) are equivalent to glmtable(seest:F) and
glmtable(Term, seest:F).  Usage of keywords 'seest' and 'sepred' is the
same as for glmtable().

For GLM functions involving a binomial response variable (logistic(),
probit(), glmfit() with dist:"binomial"), the values computed are the
estimated probabilities p of "success" associated with each cell.

In this case, you can also use keyword phrase n:N, where N is a REAL
variable, to specify the number of trials for each cell.  N can be a
scalar, a vector whose length matches the size of the table, or a matrix
or array whose dimensions match those of the table.  The resulting table
is a table of N*p.

  Cmd> logistic("y=a+b",n:100); predtable(n:100)

Caution: When the marginal table for any term in the model contains
empty cells, especially when a factor is nested in another with
different numbers of levels, the estimated means may not be what you

After fitting a non-linear model by logistic(), probit(), poisson(), or
glmfit(), when Term doesn't contain all the factors in the model,
predtable(Term) first computes the estimated marginal table in the
linear scale (logit, probit, or log) and then transforms it back into
the scale of the response.  This means that the computed marginal table
is not the marginal means of the fitted table.  For example, if b is a
factor with 3 levels, after logistic("y=a*b", n:40),
sum(predtable("a.b"))/3 is not the same as predtable("b").

When keyword phrase coefs:F was an argument on the most recent GLM
command, predtable() is not available.

See also topics anova(), anovapred(), glmpred(), glmtable(), regpred(),
modelinfo(), popmodel(), pushmodel(), 'glm'.

Gary Oehlert 2003-01-15