bayesTest: Tests for sienaBayes results with print and plot methods
In RSienaTest: Siena - Simulation Investigation for Empirical Network Analysis

Description Usage Arguments Details Value Author(s) References See Also Examples

These functions compute tests based on sienaBayesFit objects resulting from sienaBayes. Print and plot methods are available for the results of the multi-parameter test.

simpleBayesTest(z, nfirst=z$nwarm+1, tested0=0,
                probs = c(0.025,0.975), ndigits=4)
multipleBayesTest(z, testedPar, nfirst=z$nwarm+1, tested0=0, ndigits=4)
## S3 method for class 'multipleBayesTest'
print(x, descriptives=FALSE, ...)
## S3 method for class 'multipleBayesTest'
plot(x, xlim=NULL, ylim=NULL, main=NULL, ...)

`z`	A `sienaBayesFit` object, resulting from a call to `sienaBayes.`
`nfirst`	The first element of the MCMC chain used for calculating properties of the chain; this can be the first element for which it is assumed that convergence has occurred.
`tested0`	The value to be tested; for `simpleBayesTest` this must be a number (applied to all coordinates), for `multipleBayesTest` it can be a number (applied to all coordinates) or a vector.
`probs`	A vector of two numbers between 0 and 1, the credibility limits for the credibility intervals.
`ndigits`	Number of digits to be given when representing the limits of the credibility intervals.
`testedPar`	A vector with the numbers of the parameters to be tested (numbered as in the output of `simpleBayesTest`), or a `k * p` matrix, for testing `k` linear combinations given by the rows, where `p` is the number of effects in the model except the basic rate parameters.
`x`	A `multipleBayesTest` object, resulting from a call to `multipleBayesTest`.
`...`	Extra arguments for `print.multipleBayesTest` and `plot.multipleBayesTest`.
`descriptives`	Boolean: whether to print the posterior mean, s.d., and covariance matrix of the parameters included in the test.
`xlim`	Parameter `xlim` in `plot`; if `NULL`, a sensible default will be used.
`ylim`	Parameter `ylim` in `plot`; if `NULL`, a sensible default will be used.
`main`	Parameter `main` in `plot`; if `NULL`, 'posterior distances'.

Note that for the default values of probs and tested0, simpleBayesTest gives information also contained in print.sienaBayesFit.
To use multipleBayesTest, it is advisable first to execute simpleBayesTest to see the numbers that index the testedPar parameter; or its columns, if it is a matrix.
multipleBayesTest tests the hypothesis that the multivariate parameter for the effects defined by testedPar is equal to tested0. If testedPar is a set or vector of numbers then the parameters with these numbers are tested; if testedPar is a k * p matrix, the tested hypothesis is for the k linear combinations defined by its rows, and the number of columns p should be equal to the number of non-rate effects, which is the same as the number of effects listed by simpleBayesTest.
For the test, distances (for one parameter) or Mahalanobis distances (for more than one parameter) of the elements of the posterior sample from the posterior mean are calculated, and the p-value is the relative frequency that these are greater than the distance between the tested value and the posterior mean.
The p-values reported by simpleBayesTest are one-sided, and those reported by multipleBayesTest are two-sided for k=1, and 'all-sided' if k is larger than 1.
The plot presents a density plot of the posterior Mahalanobis distances, and the observed distance is indicated by a vertical line (if within the plot window).

simpleBayesTest produces a data frame containing for the non-rate effects their names, an indication of whether or not they are varying parameters, and test results. For each parameter separately, (for the varying parameters) the population mean or (for the non-varying parameters) the value is tested. The test results are the posterior credibility intervals for the probability limits defined by probs, and the posterior probabilities of values larger than tested0.
multipleBayesTest produces an object of type multipleBayesTest which is a list with values:

`prob`	posterior `p`-value
`chisquared`	test statistic
`postDistances`	sample from posterior of distances from `tested0`
`nullValue`	input value of `tested0`
`effectNames`	names of effects tested as given in ...
`posteriorSample`	sample from posterior of tested effects

print.multipleBayesTest prints the posterior p-value with an explanation; and the proportions of all sign patterns (of deviations from 0) in the sample from the posterior.
plot.multipleBayesTest plots the density function of x$postDistances.

Tom Snijders

See the manual and http://www.stats.ox.ac.uk/~snijders/siena/

sienaBayes, print.sienaBayesFit

  Group1 <- sienaDependent(array(c(N3401, HN3401), dim=c(45, 45, 2)))
  Group3 <- sienaDependent(array(c(N3403, HN3403), dim=c(37, 37, 2)))
  Group4 <- sienaDependent(array(c(N3404, HN3404), dim=c(33, 33, 2)))
  Group6 <- sienaDependent(array(c(N3406, HN3406), dim=c(36, 36, 2)))
  dataset.1 <- sienaDataCreate(Friends = Group1)
  dataset.3 <- sienaDataCreate(Friends = Group3)
  dataset.4 <- sienaDataCreate(Friends = Group4)
  dataset.6 <- sienaDataCreate(Friends = Group6)
  FourGroups <- sienaGroupCreate(
        list(dataset.1, dataset.3, dataset.4, dataset.6))
  FourEffects <- getEffects(FourGroups)
  FourEffects <- includeEffects(FourEffects, transTrip)
  FourEffects <- setEffect(FourEffects, density, random=TRUE)
  FourEffects <- setEffect(FourEffects, recip, random=TRUE)
  print(FourEffects, includeRandoms=TRUE)
  # Note this also shows the "randomEffects" column.
  FourAlgo <- sienaAlgorithmCreate(projname = "FourGroups", maxlike=TRUE)
## Not run: 
  bayes.model <- sienaBayes(FourAlgo, data = FourGroups,
        effects = FourEffects, nwarm=10, nmain=25, nrunMHBatches=10)
  bayes.model
  simpleBayesTest(bayes.model, probs = c(0.05,0.95))
  (mbt <- multipleBayesTest(bayes.model, c(2,3)))
  (mbt2 <- multipleBayesTest(bayes.model, c(2,3), tested0 = c(2,0.6)))
  plot(mbt)
  plot(mbt2)
  plot(mbt$posteriorSample)
  # Possible because the number of tested parameters is 2.
  A <- matrix(c(1,1,0),1,3)
  multipleBayesTest(bayes.model, A)

## End(Not run)