rcModelPLMr: Fit robust row-column models to a matrix

Description

These functions fit row-column effect models to matrices using PLM-r and variants

Usage

rcModelPLMr(y)
rcModelPLMrr(y)
rcModelPLMrc(y)
rcModelWPLMr(y, w)
rcModelWPLMrr(y, w)
rcModelWPLMrc(y, w)

Arguments

A numeric matrix

A matrix or vector of weights. These should be non-negative.

Value

Estimates: The parameter estimates. Stored in column effect then row effect order
Weights: The final weights used
Residuals: The residuals
StdErrors: Standard error estimates. Stored in column effect then row effect order

Details

These functions fit row-column models to the specified input matrix. Specifically the model $$y_{ij} = r_i + c_j + \epsilon_{ij}$$ with $r_i$ and $c_j$ as row and column effects respectively. Note that these functions treat the row effect as the parameter to be constrained using sum to zero.

The rcModelPLMr and rcModelWPLMr functions use the PLM-r fitting procedure. This adds column and row robustness to single element robustness.

The rcModelPLMrc and rcModelWPLMrc functions use the PLM-rc fitting procedure. This adds column robustness to single element robustness.

The rcModelPLMrr and rcModelWPLMrr functions use the PLM-rr fitting procedure. This adds row robustness to single element robustness.

Examples

Run this code

col.effects <- c(10,11,10.5,12,9.5)
row.effects <- c(seq(-0.5,-0.1,by=0.1),seq(0.1,0.5,by=0.1))


y <- outer(row.effects, col.effects,"+")
w <- runif(50)

rcModelPLMr(y)
rcModelWPLMr(y, w)


### An example where there no or only occasional outliers
y <- y + rnorm(50,sd=0.1)
par(mfrow=c(2,2))
image(1:10,1:5,rcModelPLMr(y)$Weights,xlab="row",ylab="col",main="PLM-r",zlim=c(0,1))
image(1:10,1:5,rcModelPLMrc(y)$Weights,xlab="row",ylab="col",main="PLM-rc",zlim=c(0,1))
image(1:10,1:5,rcModelPLMrr(y)$Weights,xlab="row",ylab="col",main="PLM-rr",zlim=c(0,1))
matplot(y,type="l")


### An example where there is a row outlier
y <- outer(row.effects, col.effects,"+")
y[1,] <- 11+ rnorm(5)

y <- y + rnorm(50,sd=0.1)

par(mfrow=c(2,2))
image(1:10,1:5,rcModelPLMr(y)$Weights,xlab="row",ylab="col",main="PLM-r",zlim=c(0,1))
image(1:10,1:5,rcModelPLMrc(y)$Weights,xlab="row",ylab="col",main="PLM-rc",zlim=c(0,1))
image(1:10,1:5,rcModelPLMrr(y)$Weights,xlab="row",ylab="col",main="PLM-rr",zlim=c(0,1))
matplot(y,type="l")

### An example where there is a column outlier
y <- outer(row.effects, col.effects,"+")
w <- rep(1,50)

y[,4] <- 12 + rnorm(10)
y <- y + rnorm(50,sd=0.1)

par(mfrow=c(2,2))
image(1:10,1:5,rcModelWPLMr(y,w)$Weights,xlab="row",ylab="col",main="PLM-r",zlim=c(0,1))
image(1:10,1:5,rcModelWPLMrc(y,w)$Weights,xlab="row",ylab="col",main="PLM-rc",zlim=c(0,1))
image(1:10,1:5,rcModelWPLMrr(y,w)$Weights,xlab="row",ylab="col",main="PLM-rr",zlim=c(0,1))
matplot(y,type="l")


### An example where there is both column and row outliers
y <- outer(row.effects, col.effects,"+")
w <- rep(1,50)

y[,4] <- 12 + rnorm(10)
y[1,] <- 11+ rnorm(5)

y <- y + rnorm(50,sd=0.1)

par(mfrow=c(2,2))
image(1:10,1:5,rcModelWPLMr(y,w)$Weights,xlab="row",ylab="col",main="PLM-r",zlim=c(0,1))
image(1:10,1:5,rcModelWPLMrc(y,w)$Weights,xlab="row",ylab="col",main="PLM-rc",zlim=c(0,1))
image(1:10,1:5,rcModelWPLMrr(y,w)$Weights,xlab="row",ylab="col",main="PLM-rr",zlim=c(0,1))
matplot(y,type="l")