PAsso (version 0.1.10)

residuals: Extract Model Residuals

Description

A generic function to simulate surrogate residuals for cumulative link regression models using the latent method described in Liu and Zhang (2017).

It also support the sign-based residuals (Li and Shepherd, 2010), generalized residuals (Franses and Paap, 2001), and deviance residuals for cumulative link regression models.

Usage

# S3 method for clm
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S3 method for lrm
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S3 method for orm
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S3 method for polr
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S4 method for vglm
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S4 method for vgam
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S3 method for ord
residuals(
  object,
  type = c("surrogate", "sign", "general", "deviance", "pearson", "working",
    "response", "partial"),
  jitter = c("latent", "uniform"),
  jitter.uniform.scale = c("probability", "response"),
  nsim = 1L,
  ...
)
# S3 method for PAsso
residuals(object, draw_id = 1, ...)

Arguments

object

An object of class PAsso.

type

The type of residuals which should be returned. The alternatives are: "surrogate" (default), "sign", "general", and "deviance". Can be abbreviated.

surrogate

surrogate residuals (Liu and Zhang, 2017);

sign

sign-based residuals;

general

generalized residuals (Franses and Paap, 2001);

deviance

deviance residuals (-2*loglik).

jitter

When the type = "surrogate", this argument is a character string specifying which method to use to generate the surrogate response values. Current options are "latent" and "uniform". Default is "latent".

latent

latent approach;

uniform

jittering uniform approach.

jitter.uniform.scale

When the jitter = "uniform", this is a character string specifying the scale on which to perform the jittering whenever jitter = "uniform". Current options are "response" and "probability". Default is "response".

nsim

An integer specifying the number of replicates to use. Default is 1L meaning one simulation only of residuals.

...

Additional optional arguments.

draw_id

A number refers to the i-th draw of residuals.

Value

A numeric vector of class c("numeric", "resids") containing the simulated surrogate residuals. Additionally, if nsim > 1, then the result will contain the attributes:

draws

A matrix with nsim columns, one for each is a replicate of the surrogate residuals. Note, they correspond to the original ordering of the data;

draws_id

A matrix with nsim columns. Each column contains the observation number each surrogate residuals corresponds to in draws. (This is used for plotting purposes.)

A matrix of class c("matrix", "resids") containing the simulated surrogate residuals used for the partial association analysis in PAsso. Additionally, if rep_num > 1 in PAsso, then the result will contain the attributes:

draws

An array contains all draws of residuals.

References

Liu, D., Li, S., Yu, Y., & Moustaki, I. (2020). Assessing partial association between ordinal variables: quantification, visualization, and hypothesis testing. Journal of the American Statistical Association, 1-14. 10.1080/01621459.2020.1796394

Liu, D., & Zhang, H. (2018). Residuals and diagnostics for ordinal regression models: A surrogate approach. Journal of the American Statistical Association, 113(522), 845-854. 10.1080/01621459.2017.1292915

Li, C., & Shepherd, B. E. (2010). Test of association between two ordinal variables while adjusting for covariates. Journal of the American Statistical Association, 105(490), 612-620. 10.1198/jasa.2010.tm09386

Franses, P. H., & Paap, R. (2001). Quantitative models in marketing research. Cambridge University Press. 10.1017/CBO9780511753794

Examples

# NOT RUN {
# Generate data from a quadratic probit model
set.seed(101)
n <- 2000
x <- runif(n, min = -3, max = 6)
z <- 10 + 3 * x - 1 * x^2 + rnorm(n)
y <- ifelse(z <= 0, yes = 0, no = 1)

# Scatterplot matrix
pairs(~ x + y + z)

# Misspecified mean structure
fm1 <- glm(y ~ x, family = binomial(link = "probit"))
diagnostic.plot(fm1)

# Correctly specified mean structure
fm2 <- glm(y ~ x + I(x ^ 2), family = binomial(link = "probit"))
diagnostic.plot(fm2)

# Load data
data("ANES2016")
PAsso_1 <- PAsso(responses = c("PreVote.num", "PID"),
                 adjustments = c("income.num", "age", "edu.year"),
                 data = ANES2016)

# Compute residuals
res1 <- residuals(PAsso_1)

# }