Package 'PLStests'

Model checking for high dimensional generalized linear models based on random projections

Description

The function can test goodness-of-fit of a low- or high-dimensional generalized linear model (GLM) by detecting the presence of nonlinearity in the conditional mean function of y given x using the statistics proposed by paper xx. The outputs are p-value of statisitics.

Usage

PLStests(y, x, family, b0 = 2, np = 10)

Arguments

y	: y Input matrix with n rows, 1-dimensional response vector
x	: x Input matrix with n rows, each a p-dimensional observation vector.
family	: Must be "gaussian" or "binomial" for linear or logistic regression model.
b0	: a paramter to set bindwith, the default value may better for real data analysing.
np	: the number of random projections.

Value

a list with five parameters returned. h stand for b_0. T_alpha: the p value of our statistics by random projection. T_beta: the p value of our statistic by estimated projection. T_cauchy and T_hmp are p value of two combinational method proposed by Liu and Xie (2020) and Wilson (2019) respectively. each method combines p values of np random projections.

References

Chen, W., Liu, J., Peng, H., Tan, F., & Zhu, L. (2024). Model checking for high dimensional generalized linear models based on random projections. arXiv [Stat.ME]. Retrieved from http://arxiv.org/abs/2412.10721

Examples

set.seed(100)
data("sonar_mines")
x = sonar_mines[,-1]
y = sonar_mines$y

## make y as 0 or 1 for logistic regression
class1 = "R"
class2 ="M"
y = as.character(y)
y[y==class1]=1
y[y==class2]=0
y = as.numeric(y)
y = matrix(y,ncol = 1)

## scale x  and make data to be matrix
data_test_x = x
data_test_x = as.matrix(data_test_x)
data_test_y = as.matrix(y)
data_test_x = scale(data_test_x)
PLStests(data_test_y,data_test_x,family="binomial")

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Example Dataset: sonar_mines

Description

we evaluate the proposed tests through an analysis of a classification task aimed at distinguishing between sonar signals bounced off a metal cylinder and those bounced off a roughly cylindrical rock. The dataset is available at https://archive.ics.uci.edu/dataset/151/connectionist+bench+sonar+mines+vs+rocks.

Usage

sonar_mines

Format

A data frame with 208 rows and 61 variables:

V1,V2,V3,V4,V5,V6,V7,V8,V9,V10,V11,V12,V13,V14,V15,V16,V17,V18,V19,V20,V21,V22,V23, V24,V25,V26,V27,V28,V29,V30,V31,V32,V33,V34,V35,V36,V37,V38,V39,V40,V41,V42,V43,V44,V45, V46,V47,V48,V49,V50,V51,V52,V53,V54,V55,V56,V57,V58,V59,V60

Numeric sonar signal attributes (frequencies).

y

Class label, a factor with levels 'Mine' and 'Rock'.

Source

from https://archive.ics.uci.edu/dataset/151/connectionist+bench+sonar+mines+vs+rocks

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