MDM (version 1.3)

mdm: Fits the parameteric diversity model

Description

The parametric diversity model (mdm) is a new method for directly relating diversity to environmental predictors. It is based on three components: (1) parametric diversity, a new parametric model of diversity that can represent any configuration of species proportional abundances, (2) the multinomial logit model (MLM) that can relate species proportional abundances to complex predictors and (3) the link between parametric diversity and the likelihood function of the MLM.

The mdm is fitted using the multinom package from nnet. Parametric diversities and true diversities can also be calculated for data sets using the functions eds, eds1, ed, ed1.

Usage

mdm(formula, data, weights, subset, na.action, MaxNWts, maxit = 1000, contrasts = NULL, Hess = FALSE, censored = FALSE, model = TRUE, use.shortcut = TRUE, ...)

Arguments

formula

a formula expression as for regression models, of the form response ~ predictors. The response should be a matrix with K columns comprising proportions for each of K classes. A log-linear model is fitted, with coefficients zero for the first class. An offset can be included: it should be a numeric matrix with K columns. See the documentation of formula() for other details.

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which mdm is called.

weights

optional case weights in fitting.

subset

expression saying which subset of the rows of the data should be used in the fit. All observations are included by default.

na.action

a function to filter missing data.

MaxNWts

The maximum allowable number of weights. There is no limit in the code, but MaxNWts is set to the exact number of required as specified in the formula. Thus it should not need to be changed when fitting mdm.

maxit

maximum number of iterations. Default 1000.

contrasts

a list of contrasts to be used for some or all of the factors appearing as variables in the model formula.

Hess

logical for whether the Hessian (the O/E information matrix) should be returned.

censored

If Y is a matrix with K > 2 columns, interpret the entries as one for possible classes, zero for impossible classes, rather than as counts.

model

logical. If true, the model frame is saved as component model of the returned object.

use.shortcut

logical. If true, and the model is ~1 (a constant) or ~sites (a factor with one level for each site) then the model is not fitted since the fitted values are known in each case. The first (alpha) model has fitted values equal to the input data and the second (gamma) model fits the row means. Fitting the alpha-model using nnet can be prohibitively expensive in computational time and is unneccessary. The returned models when use.shortcut == TRUE has the same components as when use.shortcut == FALSE, and hence can be used in anova tables and plotting. Using use.shortcut == TRUE can result in saving > 99% of computational time for a collection of models.

...

additional arguments for nnet.

Value

A nnet object with additional components:

deviance

the residual deviance, compared to the full saturated model (that explains individual observations exactly). Also, minus twice log-likelihood

edf

the (effective) number of degrees of freedom used by the model

AIC

the AIC for this fit

Hessian

if Hess is true

model

if model is true

entropy

the entropy of the fitted values

diversity

the diversity of the fitted values

Details

mdm calls multinom which calls nnet. The variables on the rhs of the formula should be roughly scaled to [0,1] or the fit will be slow or may not converge at all.

References

De'ath, G. (2011) The Multinomial Diversity Model: Linking Shannon Diversity To Multiple Predictors.

Ripley, B. D. (1996) Pattern Recognition and Neural Networks. Cambridge.

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth edition. Springer.

See Also

multinom, nnet

Examples

library(MDM)
data(spider6)
fit0 <- mdm(y2p(spider6[,1:6])~1,data=spider6)
fit1 <- mdm(y2p(spider6[,1:6])~Water,data=spider6)
fit2 <- mdm(y2p(spider6[,1:6])~Water+Herbs,data=spider6)
fit3 <- mdm(y2p(spider6[,1:6])~Site,data=spider6)
anova(fit0,fit1,fit2,fit3)