factanal.predictive: Probabilistically predictive factor analysis
In reo: Random effects ordination

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

A wrapper function for using the factanal function predictively. Several methods are available for exploring the predictions of fitted factor analysis models.

factanal.predictive(x, factors, ...)

## S3 method for class 'factanal.predictive'
AIC(object, ..., k = 2, corrected = TRUE)

## S3 method for class 'factanal.predictive'
biplot(x, newdata, axes=c(1,2), 
which.var=1:x$n.vars, ...)

## S3 method for class 'factanal.predictive'
deviance(object, ...)

## S3 method for class 'factanal.predictive'
logLik(object, ...)

## S3 method for class 'factanal.predictive'
pairs(x, vars = 1:x$n.vars, ls = FALSE, ...)

## S3 method for class 'factanal.predictive'
predict(object, newdata, responses = c(1), 
predictors = (1:object$n.vars)[-responses], ...)

## S3 method for class 'factanal.predictive'
scores(x, newdata, which.var=1:x$n.vars, ...)

## S3 method for class 'factanal.predictive'
screeplot(x, stat = "deviance", shift = TRUE, 
plot = TRUE, ylab, main, grey.int=0.8, ...)

`x`	For `factanal.predictive`: A data frame, numeric matrix or any object that can be coerced into a numeric matrix. Unlike `factanal`, this argument cannot be a formula or missing. For methods: An object of class `factanal.predictive`.
`object`	An object of class `factanal.predictive`.
`factors`	Number of factors to be fitted.
`k`	Not used. Included for consistency with the default method.
`corrected`	If `TRUE` the returned information criterion is corrected for small multivariate samples (called MAICc). If `FALSE` the standard AIC is returned.
`axes`	Vector of length 2 containing the numbers associated with the axes to be plotted. If the model contains only a single factor (i.e. axis), then random 'jitter' is plotted on the y-axis to improve visualisation of the plotted factor on the x-axis. If more than two axes are supplied, the first two are used with a `warning`.
`vars`	Vector giving the numbers associated with the variables to be plotted. Must contain at least two variables.
`ls`	If TRUE, the least-squares fit is also shown for comparison.
`newdata`	An optional data frame in which to look for variables with which to predict. If omitted, the fitted values are used.
`responses`	Vector giving the numbers associated with the variables to be treated as 'responses'.
`predictors`	Vector giving the numbers associated with the variables to be treated as 'predictors'.
`which.var`	Vector giving the numbers associated with the variables to be used in axis calculation.
`stat`	Character string of the name of a function that returns a statistic quantifying the 'performance' of a fitted `factanal.predictive` object. The default, deviance, results in strictly non-increasing screeplots, which is the classical behaviour of such plots. Other options are `logLik`, `AIC`, or a user-defined function.
`shift`	If `TRUE` the y-axis is shifted such that the minimum model is shifted to zero.
`plot`	If `FALSE` the plotting is suppressed.
`ylab`	Label for the y-axis. If omitted the label is taken to be `stat`.
`main`	Title for screeplot
`grey.int`	Grey colour for 'within ten units' region.
`...`	For `factanal.predictive`: Further arguments to pass to `factanal`. However, if one attempts to pass `covmat`, an error message will be produced. Unlike `factanal`, estimation cannot take place with a covariance matrix alone. This may be changed in the future. For methods: Further arguments to be passed to the default method. Note that these don't always work. I'll improve the documentation to provide a better explanation for this in the future.

An object of class factanal.predictive that includes the following components, in addition to those that are included in factanal objects:

`factors`	Either the number of factors in the model or "full" if the number of factors exceeds the maximum number for a factor analysis. If this number is exceeded, a "full" multivariate normal model is fitted that treats all covariances and variances as free parameters.
`n.obs`	Number of observations (i.e. rows in x).
`Cor`	The model-implied correlation matrix.
`call.pred`	The matched call to `factanal.predictive`.
`n.vars`	Number of variables (i.e. columns in x).
`x`	Data matrix passed to `factanal.predictive`.
`Cov`	The model-implied covariance matrix.
`B`	Unstandardized coefficients.

Steve Walker

Walker, S.C. and Jackson, D.A. (2011) Random-effects ordination: describing and predicting multivariate correlations and co-occurrences. Ecological Monographs. 81: 635-663.

This function is based on factanal. For random-effects ordination of presence-absence data see ltm.ecol.