README.md

In ying531/condinf: Conditional inference package

condinf

R package that implements conditional inference of parameters from lm and glm models. Details of conditional inference is in this paper. The current implementation uses the influence function from lm() and glm() in R and two-fold cross-fitting for conditional inference standard error estimation.

Installation

1. The devtools package has to be installed. You can install it using install.packages("devtools").
2. The latest development version can then be installied using devtools::install_github("ying531/condinf").

Helper

Usage

cond.inf(
  object,
  cond.data = NULL,
  param = NULL,
  alg = "loess",
  random.seed = NULL,
  other.params = NULL,
  folds = NULL
)

This function wraps around any lm() or glm() model. It prints the summary of conditional inference on the specified coefficients, and returns a list of results as described in the following.

| Arguments | Description | | -------------- | ------------------------------------------------------------ | | object | An object returned from lm() or glm() functions | | cond.data | Optional (recommend to provide), a dataframe for the conditioning set; set as all covariates fitted in object if not provided | | param | Optional, a vector of coefficients to conduct conditional inference; default to fit all coefficients if not provided; can be a mixture of string name and index | | alg | Optional, a string for name of algorithm, current options are 'loess' and 'grf' | | random.seed | Optional, random seed for sample splitting | | other.params | Optional, other parameters for the regression algorithm; can include span and degree for loess | | folds | Optional, a list of two folds of indices for sample splitting; can be useful to control sample splitting | | verbose | Optional, whether or not to print summary of conditional inference; default TRUE |

To use alg = 'grf' as the regressor, the R package grf is required to be installed. Also, if you do not specify alg or set alg = 'loess', then the column dimension of df.cond should be no greater than 3.

| Output | Description | | -------------- | ------------------------------------------------------------ | | cond.std.err | Estimated standard error for inference of conditional parameters | | std.err | Estimated standard error for inference of super-population parameters | | fitted.coef | Fitted (empirical) coefficient from the model | | cond.ci.low | Lower 0.95-confidence bound for conditional parameter | | cond.ci.upp | Upper 0.95-confidence bound for conditional parameter | | summary | Summary table of the model fitting results; the printed result for verbose=TRUE |

Examples

Conditional inference

Conditional inference for linear models

The following example works out conditional inference of linear regression coefficients (setting param=1 selects the intercept) for a well-specified linear model. In this case, the super-population parameter is the same as conditional parameter, and the standard errors are the same.

> X = matrix(rnorm(1000*10), nrow=1000)
> Y = X %*% matrix(c(1,2,3,rep(0,10-3)), ncol=1) + rnorm(1000) * 0.1
> Z = data.frame(X[,1:2])
> lm.mdl = lm(Y~., data = data.frame(X)) 
> cond.inf(lm.mdl, cond.data=Z, param=1)

Summary of conditional inference

                Estimate Cond. Std. Error Cond. Pr(>|z|) Sup. Std. Error Sup. Pr(>|z|)
(Intercept) 0.0001085111        0.1081838      0.9746966       0.1081838     0.9746966

In the above summary, Estimate is the original estimator, Cond. Std. Err is the estimated standard error for inferring the conditional parameter, and Cond. Pr(>|z|) is the p-value for testing whether the conditional parameter is zero. Sup. Std. Error and Sup. Pr(>|z|) are the standard error and p-value for standard super-population inference.

The following example conducts conditional inference for a misspecified linear model. In this case, the inference for the conditional parameter can be different from that for the super-population parameter (see the cond.std.err for conditional inference and std.err for super-population inference). The regression algorithm is grf and we focus on the coefficients for "X1" and "X2".

> X = matrix(rnorm(1000*10), nrow=1000)
> Y = X %*% matrix(c(1,2,3,rep(0,10-3)), ncol=1) + X[,1]**2 + rnorm(1000) * 0.1
> Z = data.frame(X[,1:2])
> lm.mdl = lm(Y~., data = data.frame(X))
> cond.inf(lm.mdl, cond.data=Z, param=c("X1", "X2"), alg='grf')

Summary of conditional inference

    Estimate Cond. Std. Error Cond. Pr(>|z|) Sup. Std. Error Sup. Pr(>|z|)
X1 0.9618222         1.893261   4.478929e-58        3.589425  2.378448e-17
X2 2.0099977         1.137924   0.000000e+00        1.423715  0.000000e+00

Conditional inference for generalized linear models

The following example works out conditional inference for parameters from a well-specified logistic model. The regression algorithm is loess. We focus on the coefficients for the second variable ("X1").

> X = matrix(rnorm(1000*10), nrow=1000)
> logit.x = X %*% matrix(c(1,2,3,rep(0,10-3)), ncol=1) + rnorm(1000) * 0.1
> Y = rbinom(1000, 1, exp(logit.x)/(1+exp(logit.x)))
> Z = data.frame(X[,1:2])
> glm.mdl = glm(Y~., data = data.frame(X), family='binomial')
> cond.inf(glm.mdl, cond.data=Z, 2)

Summary of conditional inference

  Estimate Cond. Std. Error Cond. Pr(>|z|) Sup. Std. Error Sup. Pr(>|z|)
2  1.10893         3.710156   3.332376e-21        3.710156  3.332376e-21

This is an example of conditional inference for parameters from a misspecified logistic regression model. The regression algorithm is loess. We focus on the coefficients for variable "X3" and the third variable ("X2").

> X = matrix(rnorm(1000*10), nrow=1000)
> logit.x = X %*% matrix(c(1,2,3,rep(0,10-3)), ncol=1) + X[,1]**2 + rnorm(1000) * 0.1
> Y = rbinom(n, 1, exp(logit.x)/(1+exp(logit.x)))
> Z = data.frame(X[,1:2])
> glm.mdl = glm(Y~., data = data.frame(X), family='binomial')
> cond.inf(glm.mdl, cond.data=Z, c("X3", 3))

Summary of conditional inference

   Estimate Cond. Std. Error Cond. Pr(>|z|) Sup. Std. Error Sup. Pr(>|z|)
X3 2.631113         4.492922   1.459031e-76        4.500887  2.680111e-76
X2 2.005930         4.116081   1.379739e-53        4.193597  1.088415e-51

ying531/condinf documentation built on July 29, 2022, 6:55 p.m.