eHOF: Extended HOF (Huisman-Olff-Fresco) Models

Description

Extended and enhanced hierarchical logistic regression models (called Huisman-Olff-Fresco in biology, see Huisman et al. 1993 Journal of Vegetation Science doi:10.1111/jvs.12050) models. Response curves along one-dimensional gradients including no response, monotone, plateau, unimodal and bimodal models.

Internal eHOF functions

Description

Internal eHOF functions that are not intended to be called directly, but only within other functions.

Hierarchical logistic regression

Description

Fit seven hierarchical logistic regression models and select the most appropriate model by information criteria and a bootstrap approach to guarantee model stability. The first five shapes are known as Huisman-Olff-Fresco (HOF) models in ecology (Huisman et al. 1993). Additionally the package provides two bimodal shapes.

Usage

## S3 method for class 'data.frame'
HOF(veg, grad, M = max(veg), freq.limit = 10, ...)

HOF(...)

## Default S3 method:
HOF(
  occ,
  grad,
  M = max(occ),
  y.name,
  family = binomial,
  lim = 100,
  bootstrap = 100,
  test = c("AICc", "BIC", "AIC", "Dev"),
  modeltypes = eHOF.modelnames,
  ...
)

## S3 method for class 'HOF'
coef(object, model, ...)

## S3 method for class 'HOF'
deviance(object, model, ...)

## S3 method for class 'HOF'
fitted(object, model, ...)

## S3 method for class 'HOF'
predict(object, model, newdata, ...)

pick.model(...)

## S3 method for class 'HOF'
pick.model(
  object,
  level = 0.95,
  test = c("AICc", "BIC", "AIC", "Dev"),
  modeltypes,
  penal = "df",
  gam = FALSE,
  selectMethod = c("bootselect.lower", "bootselect.always", "IC.weight", "pick.model"),
  silent = FALSE,
  ...
)

## S3 method for class 'list'
pick.model.HOF(object, ...)

Arguments

Details

The minimization function changed compared to package gravy (Oksanen 2002) from nlm to nlminb to be able to set a limit for estimated parameters (default= -100 to 100). The old models III and V have been often too sharp, lim=Inf will produce results similar to gravy. Function [pick.model()] finds the most adequate modeltype according to the chosen Information Criterion (AICc is default). Function fitted returns the fitted values for the used gradient, and predict for any values in newdata.

To improve and check model stability a bootstrapping mechanism is implemented in function HOF. If the initially chosen model type is different from the most frequent one, the latter will be chosen by default. Bootstrapping is done with sample(length(grad), replace = TRUE).

Value

HOF.fit returns an object of class "HOF" which contains the parameters of the call, the fitting results for every model type and a vector of chosen model types from bootstrapping.

Author(s)

Florian Jansen, Jari Oksanen

References

Jansen, F. & Oksanen, J. (2013) What shape are species responses along ecological gradients? - Huisman-Olf-Fresco models revisited. Journal of Vegetation Science, DOI: 10.1111/jvs.12050

Oksanen, J. & Minchin, P.R. (2002). Continuum theory revisited: what shape are species responses along ecological gradients? Ecological Modelling 157, 119-129.

Huisman, J., Olff, H. & Fresco, L.F.M. (1993). A hierarchical set of models for species response analysis. Journal of Vegetation Science 4, 37-46.

See Also

[plot.HOF()] provides advanced plotting schemes for HOF models. [Para()] derives model parameters like optimum, niche (width), slope etc.

Examples

  data(acre)
  sel <- c('MATRREC', 'RUMEACT', 'SILENOC', 'APHAARV', 'MYOSARV', 'DESUSOP', 'ARTE#VU')
  mo <- HOF(acre[,match(sel, names(acre))], acre.env$PH_KCL, M = 1, bootstrap = NULL)
  mo

Curve parameters of eHOF models

Description

Derive common shape parameters from the different model types. Calculate a set of parameters (see values below) from eHOF models.

Usage

Para(resp, ...)

## S3 method for class 'HOF'
Para(resp, model, newdata = NULL, ...)

Arguments

Details

For models VI and VII Para will give you two expectancy values for the ranges left and right of the pessimum between the model optima. If you want to have the overall expectancy value, use: gradient <- seq(min(Para(resp)$range), max(Para(resp)$range), length.out=10000) weighted.mean(gradient, predict(resp, newdata=gradient))

Value

* species Name or abbreviat of the species. * abund sum Abundance sum, i.e. sum of all response values divided by M. * range Range of x values. * model Model type, if not specified the result of [pick.model]. * para Model parameters (a to d). * M Maximum response value, specified in the HOF function call. * mini Location of the minimum, i.e. the gradient value, where the response is lowest, for model VI and VII the lowest response between the two optima. * pess Lowest estimated response value. * top Highest estimated response value(s). * opt Location of the optimum, i.e. the gradient value, where the species response is highest. NA for model I and an optimum interval for model type III. * expect Expectancy value, i.e. average x value under the model curve). * max slope Highest slope, i.e. maximum of the first derivation of the curve. * centralBorder Following Heegard, the central borders are calculated as the gradient values, where the response reaches "exp(-1/2)" of the top. * outerBorder Following Heegard, the outer borders of the species niche are calculated as the gradient values, where the response reaches exp(-2) of the top. * raw mean Average of measured x values.

Author(s)

Florian Jansen

References

Heegard, E. (2002) The outer border and central border for species-environmental relationships estimated by non-parametric generalised additive models. Ecological Modelling, 157, 131-139.

Damgaard, C. (2006) Modelling ecological presence-absence data along an environmental gradient: threshold levels of the environment. Environ Ecol Stat 13:229-236.

Curve derivatives of eHOF models

Description

Slope and inflection points for the eHOF model types.

Usage

Para_deriv(
  resp,
  newdata = NULL,
  model = NULL,
  p,
  type = c("slope", "inflection"),
  ...
)

Arguments

Value

For slope a vector of slopes for all newdata points. Inflection points are the extremes of the second derivative.

Author(s)

Florian Jansen

References

Peper, J., Jansen, F., Pietzsch, D., Manthey, M. 2011. Patterns of plant species turnover along grazing gradients. Journal of Vegetation Science 22: 457–466.

Vegetation plots from arable fields in North-Eastern Germany

Description

Species and Environmental Data from arable fields in North-Eastern Germany. The data contains 100 selected plots (rows) and 6 species (columns).

Usage

data(acre)

Format

Two data frames, one data frame called acre with 100 vegetation plots (rows). Species are named with 7 letter shortletters according to the taxonomic reference list GermanSL. Plant performance is given as presence-absence. The second data frame, named acre.env consists of plot information about date of survey, survey area, total plant cover and measured soil pH.

Details

Soil pH was measured in 1-mol KCl buffer solution.

References

Manthey, M. (2003). Vegetations\"okologie der \"Acker und Ackerbrachen Mecklenburg-Vorpommerns. 209 p., Berlin [u.a.]: Cramer.

Examples

 data(acre)
 hist(acre.env$PH_KCL)
 ## Not run: 
 vignette('eHOF', 'eHOF')

## End(Not run)

Automatically Specifying Complex Plot Arrangements

Description

Automatic version of function layout for given number of subplots. Defined matrix schemes for layout for up to 32 subfigures.

Usage

autolayout(N, byrow = TRUE, ...)

Arguments

Value

Number of figures, N, see layout.

Examples

for(i in sample(1:32, 1)) {
 autolayout(i, byrow=TRUE)
 layout.show(i)
 }

Beta response models

Description

Generating beta response models. Implemented to compare the hierarchical logistic regression models with beta response models.

Usage

betaresp(x, p1, p2, alpha, gamma, hi)

Arguments

Author(s)

Jari Oksanen

Examples

 x <- seq(0,3, len=201)
 m <- betaresp(x, 2, 0.8, 0.1, 0.5, 0.8)
 plot(m)

Extended HOF (Huisman-Olff-Fresco) Models

Description

Extended and enhanced hierarchical logistic regression models (called Huisman-Olff-Fresco in biology, see Huisman et al. 1993 Journal of Vegetation Science <doi:10.1111/jvs.12050>) models. Response curves along one-dimensional gradients including no response, monotone, plateau, unimodal and bimodal models.

References

Jansen, F., Dengler, J (2011) Plant names in vegetation databases - a neglected source of bias, Journal of vegetation science, 21(6), 1179-1186. http://dx.doi.org/10.1111/j.1654-1103.2010.01209.x

Species Data and Altitude from Mt. Field, Tasmania

Description

Species and Environmental Data from Mt. Field, Tasmania. The acre data frame has 100 selected sites (rows) and 6 species (columns). Data frame mtf.env has only one variable: Altitude above sea level (in meters) for each site. The data are a subset of well drained sites from a more extensive data set.

Usage

 data(mtf)

Format

The species data frame contains the following species:

EPACSERP

a numeric vector

CYATPETI

a numeric vector

NOTHCUNN

a numeric vector

POA.GUNN

a numeric vector

BAUERUBI

a numeric vector

References

Minchin, P.R. (1989). Montane vegetation of the Mt. Field massif, Tasmania: a test of some hypotheses about properties of community patterns. Vegetatio 83, 97.110.

Examples

 data(mtf)

Plot Hierarchical Logistic Regression Models

Description

Plot single or multiple HOF models with or without model parameters.

Usage

## S3 method for class 'HOF'
plot(
  x,
  marginal = c("bar", "rug", "hist", "points", "n"),
  boxp = TRUE,
  las.h = 1,
  yl,
  main,
  model,
  test = "AICc",
  modeltypes,
  onlybest = TRUE,
  penal,
  gam = FALSE,
  selectMethod,
  silent = FALSE,
  para = FALSE,
  gam.se = FALSE,
  color,
  newdata = NULL,
  lwd = 1,
  leg = TRUE,
  add = FALSE,
  xlabel,
  ...
)

Arguments

Details

Plottype layout will give a normal plot for a single species, or if the HOF object contains several species, the graphics display will be divided by autolayout. Multiple species can also be plotted by a lattice xyplot and plotted with plot.HOF for every species. The third option (plottype='all') plots all selected species on the same graph which might be useful to evaluate e.g. the species within one vegetation plot, see examples.

A rug adds a rug representation (1-d plot) of the data to the plot. A rug plot is a compact way of illustrating the marginal distributions of x. Positions of the data points along x and y are denoted by tick marks, reminiscent of the tassels on a rug. Rug marks are overlaid onto the axis. A dit='bar' plot will display the original response values. For binary data this will be identical to rug.

Author(s)

Florian Jansen

References

de la Cruz Rot M (2005) Improving the Presentation of Results of Logistic Regression with R. Bulletin of the Ecological Society of America 86: 41-48

See Also

[HOF()]

Examples

  data(acre)
  sel <- c('MATRREC', 'RUMEACT', 'SILENOC', 'APHAARV', 'MYOSARV', 'DESUSOP', 'ARTE#VU')
  mo <- HOF(acre[match(sel, names(acre))], acre.env$PH_KCL, M=1, bootstrap=NULL)
  par(mar=c(2,2,1,.1))
  plot(mo, para=TRUE)

  #' An example for plottype='all' to show species responses for the species within
  #' the most acidic and the most calcareous vegetation plot.
  ## Not run: 
    allSpeciesFromAnAcidicPlot <- acre['57',] > 0
    mods.acidic <- HOF(acre[,allSpeciesFromAnAcidicPlot],acre.env$PH_KCL,M=1,bootstrap=NULL)
    allSpeciesFromAnCalcareousPlot <- acre['87',] > 0
    mods.calc <- HOF(acre[,allSpeciesFromAnCalcareousPlot],acre.env$PH_KCL,M=1,bootstrap=NULL)

    autolayout(2)
    plot(mods.acidic, plottype='all', main='Plot with low pH')
    abline(v=acre.env$PH_KCL[acre.env$RELEVE_NR == '57'])
    names(mods.acidic)

    plot(mods.calc, plottype='all', main='Plot with high pH')
    abline(v=acre.env$PH_KCL[acre.env$RELEVE_NR == '87'])
    names(mods.calc)
  
## End(Not run)