regdiag {freqparcoord}

Diagnosing regression model fit using parallel coordinates.

Description

Performs parametric regression model fit diagnostics, based on freqparcoord. One axis is the "divergences," the differences beween the parametric and nonparametric estimates of the population regression function, while the other axes are the predictor variables. Note that the divergences are NOT the parametric model residuals, e.g. differences between fitted model values and response ("Y") values.

The question addressed is, "In what regions of predictor space is the parametric fit poorer?" To answer that, the divergences are grouped into upper and lower tails; e.g. if tail is set to 0.10, we find the data points that have divergences in the lower and upper 10%, then plot both groups, as well as the middle.

The parallel coordinates plot then can be used to identify regions in which the parametric model tends to either under- or overpredict the response, thus indicating possible addition of interaction or polynomial terms.

Furthermore, in the case for regdiag in which an lm object is input, the adjusted R-squared value for the parametric model and the R-squared value from the nonparametric fit are computed. If the nonparametric value is substantially larger than the parametric one, this is an indication of some deficiency in the parametric model, thus providing some quantitative information on whether inclusion of interaction and/or polynomial terms may be useful.

The term regression is used in the sense of condtional mean response given the predictors. Thus parametric classification models such as the logistic may also be used, with the regression function being the condtional probability of response = 1, given the predictors.

Usage

regdiag(regout, tail=0.10, k=NULL, m=5,
      checkna = TRUE, cls = NULL, nchunks = length(cls))
regdiagbas(preds, resp, parest, tail=0.10, k=NULL, m=5,
      checkna = TRUE, cls = NULL, nchunks = length(cls))

Arguments

regout

Output of lm or glm

preds

Matrix of predictor values.

resp

Vector of response values.

parest

Parametric model estimates of the population regression function at the predictor data points.

tail

Proportion of most negative and most positive divergences to use in grouping.

k

See freqparcoord.

m

See freqparcoord.

checkna

See freqparcoord.

cls

See freqparcoord.

nchunks

See freqparcoord.

Details

The population regression function (including the case of a probability function in a classification problem) is estimated nonparametrically at the observation points, using knnreg.

The nonparametric estimates are subtracted from the parametric ones, yielding the divergences. A frequency-parallel coordinates plot is displayed as described above.

The R-squared values are available in the situation noted earlier. The nonparametric R-squared value is calculated as the squared correlation between estimated regression value and the response value.

It is possible that in one of the tail groups the response value is constant, in which case an error message appears. If so, try a larger value of tail.

Value

An object of type "gg" (a ggplot2 object, displays when printed), with new components added:

• The nonparametric regression estimates, in nonparest.

• In the case of a linear model specified via regout, the adjusted R-squared value for the parametric model, in paramr2, and nonparamr2, the R-squared value from the nonparametric fit. The latter is the squared correlation between predicted and actual response values

Author(s)

Norm Matloff <[e-mail]> and Yingkang Xie <[e-mail]>

Examples

data(mlb)

lmout <- lm(mlb$Weight ~ mlb$Height + mlb$Age)
p <- regdiag(lmout,0.10,k=50,m=25)
p
# taller, older players are overpredicted, with shorter, younger players
# underpredicted; suggests that adding quadratic terms for Height, Age
# may help in the tails
# let's compare the R-squared values
p$paramr2 
p$nonparamr2 
# not much difference (param. model a bit better), possibly due to 
# small sample size 

# doing it "the long way" (showing use without an lm/glm object)
parest <- lmout$fitted.values
regdiagbas(mlb[c("Height","Age")], mlb$Weight,parest,0.10,k=50,m=25)

data(prgeng)
pg <- prgeng
pg1 <- pg[pg$wageinc >= 40000 & pg$wkswrkd >= 48,]
l1 <- lm(wageinc ~ age+educ+sex,data=pg1)
p <- regdiag(l1)
p
p$paramr2
p$nonparamr2
# young men's wages underpredicted, older women overpredicted; both
# R-squared values low, but nonpar is about 27% higher, indicating room
# for improvement; interaction and polynomial terms may help

## Not run: 
data(newadult)
g1 <- glm(gt50 ~ edu + age + gender + mar, data=newadult, family=binomial)
regdiag(g1)
# parametric model underpredicts older highly-educated married men,
# and overpredicts young female lesser-educated singles; might try adding 
# interaction terms 

## End(Not run)