logistic.regression: Logistic and Auto-logistic regression

Description

Performs a logistic (binomial) or auto-logistic (spatially lagged binomial) regression using maximum likelihood or penalized maximum likelihood estimation.

It should be noted that the auto-logistic model (Besag 1972) is intended for exploratory analysis of spatial effects. Auto-logistic are know to underestimate the effect of environmental variables and tend to be unreliable (Dormann 2007). Wij matrix options under style argument - B is the basic binary coding, W is row standardized (sums over all links to n), C is globally standardized (sums over all links to n), U is equal to C divided by the number of neighbours (sums over all links to unity) and S is variance-stabilizing. Spatially lagged y defined as: W(y)ij=sumj_(Wij yj)/ sumj_(Wij) where; Wij=1/Euclidean(i,j) If the object passed to the function is an sp class there is no need to call the data slot directly via "object@data", just pass the object name.

Usage

logistic.regression(
  ldata,
  y,
  x,
  penalty = TRUE,
  autologistic = FALSE,
  coords = NULL,
  bw = NULL,
  type = "inverse",
  style = "W",
  longlat = FALSE,
  ...
)

Arguments

ldata

data.frame object containing variables

Dependent variable (y) in ldata

Independent variable(s) (x) in ldata

penalty

Apply regression penalty (TRUE/FALSE)

autologistic

Add auto-logistic term (TRUE/FALSE)

coords

Geographic coordinates for auto-logistic model matrix or sp object.

Distance bandwidth to calculate spatial lags (if empty neighbors result, need to increase bandwidth). If not provided it will be calculated automatically based on the minimum distance that includes at least one neighbor.

type

Neighbor weighting scheme (see autocov_dist)

style

Type of neighbor matrix (Wij), default is mean of neighbors

longlat

Are coordinates (coords) in geographic, lat/long (TRUE/FALSE)

...

Additional arguments passed to lrm

Value

A list class object with the following components:

model - lrm model object (rms class)
bandwidth - If AutoCov = TRUE returns the distance bandwidth used for the auto-covariance function
diagTable - data.frame of regression diagnostics
coefTable - data.frame of regression coefficients
Residuals - data.frame of residuals and standardized residuals
AutoCov - If an auto-logistic model, AutoCov represents lagged auto-covariance term

References

Besag, J.E., (1972) Nearest-neighbour systems and the auto-logistic model for binary data. Journal of the Royal Statistical Society, Series B Methodological 34:75-83

Dormann, C.F., (2007) Assessing the validity of autologistic regression. Ecological Modelling 207:234-242

Le Cessie, S., Van Houwelingen, J.C., (1992) Ridge estimators in logistic regression. Applied Statistics 41:191-201

Shao, J., (1993) Linear model selection by cross-validation. JASA 88:486-494

Examples

Run this code

# NOT RUN {
require(sp)
require(spdep)
require(rms)                                                                       
data(meuse)
  coordinates(meuse) <- ~x+y  
    meuse@data <- data.frame(DepVar=rbinom(dim(meuse)[1], 1, 0.5), 
                              meuse@data)

#### Logistic model
lmodel <- logistic.regression(meuse, y='DepVar', 
                  x=c('dist','cadmium','copper')) 
  lmodel$model
    lmodel$diagTable
      lmodel$coefTable

#### Logistic model with factorial variable
lmodel <- logistic.regression(meuse, y='DepVar', 
            x=c('dist','cadmium','copper', 'soil')) 
  lmodel$model
    lmodel$diagTable
      lmodel$coefTable

### Auto-logistic model using 'autocov_dist' in 'spdep' package
lmodel <- logistic.regression(meuse, y='DepVar', 
            x=c('dist','cadmium','copper'), autologistic=TRUE, 
            coords=coordinates(meuse), bw=5000) 
  lmodel$model
    lmodel$diagTable
      lmodel$coefTable
  est <- predict(lmodel$model, type='fitted.ind')

#### Add residuals, standardized residuals and estimated probabilities
VarNames <- rownames(lmodel$model$var)[-1]
  meuse@data$AutoCov <- lmodel$AutoCov
    meuse@data <- data.frame(meuse@data, Residual=lmodel$Residuals[,1], 
                     StdResid=lmodel$Residuals[,2], Probs=predict(lmodel$model, 
                     meuse@data[,VarNames],type='fitted') )  

#### Plot fit and probabilities
resid(lmodel$model, "partial", pl="loess") 
# plot residuals
resid(lmodel$model, "partial", pl=TRUE) 

# global test of goodness of fit 
resid(lmodel$model, "gof")

# Approx. leave-out linear predictors
lp1 <- resid(lmodel$model, "lp1")            

# Approx leave-out-1 deviance            
-2 * sum(meuse@data$DepVar * lp1 + log(1-plogis(lp1)))

# plot estimated probabilities at points
spplot(meuse, c('Probs'))


# }