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Last data update: 2014.03.03

R: Fits the parameteric diversity model

mdm	R Documentation

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.

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.

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

Note

mdm is a modifed version of multinom in the nnet package.

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.

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)

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(MDM)
Loading required package: nnet
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MDM/mdm.Rd_%03d_medium.png", width=480, height=480)
> ### Name: mdm
> ### Title: Fits the parameteric diversity model
> ### Aliases: mdm
> ### Keywords: mdm
> 
> ### ** Examples
> 
> library(MDM)
> data(spider6)
> fit0 <- mdm(y2p(spider6[,1:6])~1,data=spider6)
# weights:  12 (5 variable)
> fit1 <- mdm(y2p(spider6[,1:6])~Water,data=spider6)
# weights:  18 (10 variable)
initial  value 50.169265 
iter  10 value 38.780815
iter  20 value 38.409944
final  value 38.409941 
converged
> fit2 <- mdm(y2p(spider6[,1:6])~Water+Herbs,data=spider6)
# weights:  24 (15 variable)
initial  value 50.169265 
iter  10 value 36.791764
iter  20 value 35.415854
iter  30 value 35.415361
final  value 35.415361 
converged
> fit3 <- mdm(y2p(spider6[,1:6])~Site,data=spider6)
# weights:  174 (140 variable)
> anova(fit0,fit1,fit2,fit3)
Deviances, Entropies and Diversities of Parametric Diversity Models

Response: y2p(spider6[, 1:6]) 

Model 1: y2p(spider6[, 1:6]) ~ 1
Model 2: y2p(spider6[, 1:6]) ~ Water
Model 3: y2p(spider6[, 1:6]) ~ Water + Herbs
Model 4: y2p(spider6[, 1:6]) ~ Site 

   DF DF-Diff    Dev Dev-Diff    Ent Ent-Diff    Div Div-Ratio
1 135         94.105          1.6804          5.3680          
2 130       5 76.820  17.2856 1.3718  0.30867 3.9424    1.3616
3 125       5 70.831   5.9892 1.2648  0.10695 3.5425    1.1129
4   0     125 60.923   9.9075 1.0879  0.17692 2.9681    1.1935
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>