ordFusion: Fusion and selection of dummy coefficients of ordinal...

In ordPens: Selection, Fusion, Smoothing and Principal Components Analysis for Ordinal Variables

Fusion and selection of dummy coefficients of ordinal predictors

Description

Fits dummy coefficients of ordinally scaled independent variables with a fused lasso penalty on differences of adjacent dummy coefficients. Using the ordinalNet algorithm if cumulative logit model is fitted, otherwise glmpath algorithm is used.

Usage

ordFusion(x, y, u = NULL, z = NULL, offset = rep(0,length(y)), lambda,  
  model = c("linear", "logit", "poisson", "cumulative"), 
  restriction = c("refcat", "effect"), scalex = TRUE, nonpenx = NULL, 
  frac.arclength = NULL, ...)

Arguments

x	the matrix of ordinal predictors, with each column corresponding to one predictor and containing numeric values from {1,2,...}; for each covariate, category 1 is taken as reference category with zero dummy coefficient.
y	the response vector.
u	a matrix (or data.frame) of additional categorical (nominal) predictors, with each column corresponding to one (additional) predictor and containing numeric values from {1,2,...}; corresponding dummy coefficients will not be penalized, and for each covariate category 1 is taken as reference category. Curretnly not supported if model == "cumulative".
z	a matrix (or data.frame) of additional metric predictors, with each column corresponding to one (additional) predictor; corresponding coefficients will not be penalized. Curretnly not supported if model == "cumulative".
offset	vector of offset values.
lambda	vector of penalty parameters, i.e., lambda values.
model	the model which is to be fitted. Possible choices are "linear" (default), "logit", "poisson" or "cumulative". See details below.
restriction	identifiability restriction for dummy coding. "reference" takes category 1 is as reference category (default), while with "effect" dummy coefficients sum up to 0 (known as effect coding).
scalex	logical. Should (split-coded) design matrix corresponding to x be scaled to have unit variance over columns before fitting? See details below.
nonpenx	vectors of indices indicating columns of x whose regression coefficients are not penalized. Curretnly not supported if model == "cumulative".
frac.arclength	just in case the corresponding glmpath argument is to be modified; default is 1 for model == "linear", and 0.1 otherwise.
...	additional arguments to ordinalNet (if model == "cumulative") or glmpath.

Details

The method assumes that categorical covariates (contained in x and u) take values 1,2,...,max, where max denotes the (columnwise) highest level observed in the data. If any level between 1 and max is not observed for an ordinal predictor, a corresponding (dummy) coefficient is fitted anyway (by linear interpolation, due to some additional but small quadratic penalty, see glmpath for details). If any level > max is not observed but possible in principle, and a corresponding coefficient is to be fitted, the easiest way is to add a corresponding row to x (and u,z) with corresponding y value being NA.

If a linear regression model is fitted, response vector y may contain any numeric values; if a logit model is fitted, y has to be 0/1 coded; if a poisson model is fitted, y has to contain count data. If a cumulative logit model is fitted, y takes values 1,2,...,max.

If scalex is TRUE, (split-coded) design matrix constructed from x is scaled to have unit variance over columns (see standardize argument of glmpath or/and ordinalNet).

Value

An ordPen object, which is a list containing:

fitted	the matrix of fitted response values of the training data. Columns correspond to different lambda values.
coefficients	the matrix of fitted coefficients with respect to dummy-coded (ordinal or nominal) categorical input variables (including the reference category) as well as metric predictors. Columns correspond to different lambda values.
model	the type of the fitted model: "linear", "logit", "poisson", or "cumulative".
restriction	the type of restriction used for identifiability.
lambda	the used lambda values.
xlevels	a vector giving the number of levels of the ordinal predictors.
ulevels	a vector giving the number of levels of the nominal predictors (if any).
zcovars	the number of metric covariates (if any).

Author(s)

Jan Gertheiss, Aisouda Hoshiyar

References

Gertheiss, J. and G. Tutz (2010). Sparse modeling of categorial explanatory variables. The Annals of Applied Statistics, 4, 2150-2180.

Hoshiyar, A., Gertheiss, L.H., and Gertheiss, J. (2023). Regularization and Model Selection for Item-on-Items Regression with Applications to Food Products' Survey Data. Preprint, available from https://arxiv.org/abs/2309.16373.

Park, M.Y. and T. Hastie (2007). L1 regularization path algorithm for generalized linear models. Journal of the Royal Statistical Society B, 69, 659-677.

Tutz, G. and J. Gertheiss (2014). Rating scales as predictors – the old question of scale level and some answers. Psychometrica, 79, 357-376.

Tutz, G. and J. Gertheiss (2016). Regularized regression for categorical data. Statistical Modelling, 16, 161-200.

See Also

plot.ordPen, predict.ordPen, ICFCoreSetCWP

Examples

# fusion and selection of ordinal covariates on a simulated dataset
set.seed(123)

# generate (ordinal) predictors
x1 <- sample(1:8,100,replace=TRUE)
x2 <- sample(1:6,100,replace=TRUE)
x3 <- sample(1:7,100,replace=TRUE)

# the response
y <- -1 + log(x1) + sin(3*(x2-1)/pi) + rnorm(100)

# x matrix
x <- cbind(x1,x2,x3)

# lambda values
lambda <- c(80,70,60,50,40,30,20,10,5,1) 

# fusion and selection
ofu <- ordFusion(x = x, y = y, lambda = lambda)

# results
round(ofu$coef,digits=3)
plot(ofu)

# If for a certain plot the x-axis should be annotated in a different way,
# this can (for example) be done as follows:
plot(ofu, whx = 1, xlim = c(0,9), xaxt = "n")
axis(side = 1, at = c(1,8), labels = c("no agreement","total agreement"))

ordPens documentation built on Oct. 10, 2023, 5:07 p.m.