gnm (version 1.1-5)

getContrasts: Estimated Contrasts and Standard Errors for Parameters in a gnm Model

Description

Computes contrasts or scaled contrasts for a set of (non-eliminated) parameters from a gnm model, and computes standard errors for the estimated contrasts. Where possible, quasi standard errors are also computed.

Usage

getContrasts(model, set = NULL,  ref = "first", scaleRef = "mean",
  scaleWeights = NULL, dispersion = NULL, check = TRUE, ...)

Value

An object of class

qv --- see qvcalc.

Arguments

model

a model object of class "gnm".

set

a vector of indices (numeric) or coefficient names (character). If NULL, a dialog will open for parameter selection.

ref

either a single numeric index, or a vector of real numbers which sum to 1, or one of the character strings "first", "last" or "mean".

scaleRef

as for ref

scaleWeights

either NULL, a vector of real numbers, "unit" or "setLength".

dispersion

either NULL, or a positive number by which the model's variance-covariance matrix should be scaled.

check

TRUE or FALSE or a numeric vector -- for which of the specified parameter combinations should estimability be checked? If TRUE, all are checked; if FALSE, none is checked.

...

arguments to pass to other functions.

Author

David Firth and Heather Turner

Details

The indices in set must all be in 1:length(coef(object)). If set = NULL, a dialog is presented for the selection of indices (model coefficients).

For the set of coefficients selected, contrasts and their standard errors are computed. A check is performed first on the estimability of all such contrasts (if check = TRUE) or on a specified subset (if check is a numeric index vector). The specific contrasts to be computed are controlled by the choice of ref: this may be "first" (the default), for contrasts with the first of the selected coefficients, or "last" for contrasts with the last, or "mean" for contrasts with the arithmetic mean of the coefficients in the selected set; or it may be an arbitrary vector of weights (summing to 1, not necessarily all non-negative) which specify a weighted mean against which contrasts are taken; or it may be a single index specifying one of the coefficients with which all contrasts should be taken. Thus, for example, ref = 1 is equivalent to ref = "first", and ref = c(1/3, 1/3, 1/3) is equivalent to ref = "mean" when there are three coefficients in the selected set.

The contrasts may be scaled by $$\frac{1}{\sqrt{\sum_r v_r * d_r^2}}$$ where \(d_r\) is a contrast of the r'th coefficient in set with the reference level specified by scaleRef and \(v\) is a vector of weights (of the same length as set) specified by scaleWeights. If scaleWeights is NULL (the default), scaleRef is ignored and no scaling is performed. Other options for scaleWeights are "unit" for weights equal to one and "setLength" for weights equal to the reciprocal of length(set). If scaleRef is the same as ref, these options constrain the sum of squared contrasts to 1 and length(set) respectively.

Quasi-variances (and corresponding quasi standard errors) are reported for unscaled contrasts where possible. These statistics are invariant to the choice of ref, see Firth (2003) or Firth and Menezes (2004) for more details.

References

Firth, D (2003). Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1--18.

Firth, D and Menezes, R X de (2004). Quasi-variances. Biometrika 91, 65--80.

See Also

gnm, se.gnm, checkEstimable, qvcalc, ofInterest

Examples

### Unscaled contrasts ###
set.seed(1)

## Fit the "UNIDIFF" mobility model across education levels -- see ?yaish
unidiff <- gnm(Freq ~ educ*orig + educ*dest +
               Mult(Exp(educ), orig:dest),
               ofInterest = "[.]educ", family = poisson,
               data = yaish,  subset = (dest != 7))
## Examine the education multipliers (differences on the log scale):
unidiffContrasts <- getContrasts(unidiff, ofInterest(unidiff))
plot(unidiffContrasts,
  main = "Unidiff multipliers (log scale): intervals based on
           quasi standard errors",
  xlab = "Education level", levelNames = 1:5)


### Scaled contrasts (elliptical contrasts) ###
set.seed(1)

##  Goodman Row-Column association model fits well (deviance 3.57, df 8)
mentalHealth$MHS <- C(mentalHealth$MHS, treatment)
mentalHealth$SES <- C(mentalHealth$SES, treatment)
RC1model <- gnm(count ~ SES + MHS + Mult(SES, MHS),
                family = poisson, data = mentalHealth)
## Row scores and column scores are both unnormalized in this
## parameterization of the model 

## The scores can be normalized as in Agresti's eqn (9.15):
rowProbs <- with(mentalHealth, tapply(count, SES, sum) / sum(count))
colProbs <- with(mentalHealth, tapply(count, MHS, sum) / sum(count))
mu <- getContrasts(RC1model, pickCoef(RC1model, "[.]SES"),
                   ref = rowProbs, scaleRef = rowProbs,
                   scaleWeights = rowProbs)
nu <- getContrasts(RC1model, pickCoef(RC1model, "[.]MHS"),
                   ref = colProbs, scaleRef = colProbs,
                   scaleWeights = colProbs)
all.equal(sum(mu$qv[,1] * rowProbs), 0)
all.equal(sum(nu$qv[,1] * colProbs), 0)
all.equal(sum(mu$qv[,1]^2 * rowProbs), 1)
all.equal(sum(nu$qv[,1]^2 * colProbs), 1)