Fit robust row-column models to a matrix
These functions fit row-column effect models to matrices using PLM-r and variants
rcModelPLMr(y) rcModelPLMrr(y) rcModelPLMrc(y) rcModelWPLMr(y, w) rcModelWPLMrr(y, w) rcModelWPLMrc(y, w)
y |
A numeric matrix |
w |
A matrix or vector of weights. These should be non-negative. |
These functions fit row-column models to the specified input matrix. Specifically the model
y_ij = r_i + c_j + e_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.
A list with following items:
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 |
B. M. Bolstad bmb@bmbolstad.com
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")
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