learnIQ1var: IQ-learning: contrast variance modeling

In iqLearn: Interactive Q-Learning

Description

Estimates the variance function of the contrast function by fitting a constant variance function or a log linear model to the residuals of the contrast mean fit.

Usage

learnIQ1var(object, ...)

## S3 method for class 'formula'
learnIQ1var(formula, data, treatName, intNames,
method, cmObject, ...)
## Default S3 method:
learnIQ1var(object, H1CVar, s1sInts, method, ...)

Arguments

formula	right-hand side formula containing the linear model to be used for the log-transformed, squared residuals from the contrast function mean fit
data	data frame containing variables used in formula
treatName	character string indicating the stage 1 treatment name
intNames	vector of characters indicating the names of the variables that interact with the stage 1 treatment in the contrast function variance model
method	either "homo" for a constant variance function or "hetero" for a log-linear variance function; default method is "homo"
cmObject	object of type learnIQ1cm
object	object of type learnIQ1cm
H1CVar	matrix or data frame of first-stage covariates to include as main effects in the log-linear model; default is NULL for a constant variance fit
s1sInts	indices pointing to columns of H1CVar that should be included as treatment interaction effects in the log-linear model; default is NULL
...	additional arguments to be passed to lm() when fitting the hetero log-linear model

Details

If method="homo", computes the variance of the residuals from the contrast function mean fit. If method="hetero", fits a model of the form

E (log e^2 | H1, A1) = H10^Tγ0 + A1*H11^Tγ1

where H10 and H11 are summaries of H1. Though a slight abuse of notation, these summaries are not required to be the same as H10 and H11 in the main effect term regression or the contrast mean fit. Also, e^2 = H21^Tβ21 - E(H21^T β21 | H1, A1). For an object of type learnIQ1var, summary(object) and plot(object) can be used for evaluating model fit.

Value

stdDev	standard deviation of the residuals from the contrast function mean fit when method="homo", otherwise NULL
stdResids	standardized residuals of the contrast function after mean and variance modeling, using either method="homo" or "hetero"
gammaHat0	estiamted regression coefficients from the log-linear model main effects when method="hetero", otherwise NULL
gammaHat1	estimated regression coefficients from the log-linear model interaction effects when method="hetero", otherwise NULL
s1VarFit	lm() object from the log-linear model when method="hetero", otherwise NULL
homo	logical variable indicating if method="homo" was used
sigPos	vector of predicted values when A1=1 for all patients
sigNeg	vector of predicted values when A1=-1 for all patients
s1sInts	indices of variables in H1CVar included as treatment interactions in the model; same as input s1sInts

Author(s)

Kristin A. Linn <[e-mail]>, Eric B. Laber, Leonard A. Stefanski

References

Linn, K. A., Laber, E. B., Stefanski, L. A. (2015) "iqLearn: Interactive Q-Learning in R", Journal of Statistical Software, 64(1), 1–25.

Laber, E. B., Linn, K. A., and Stefanski, L. A. (2014) "Interactive model building for Q-learning", Biometrika, 101(4), 831-847.

See Also

learnIQ1cm, iqResids

Examples

## load in two-stage BMI data
data (bmiData)
bmiData$A1[which (bmiData$A1=="MR")] = 1
bmiData$A1[which (bmiData$A1=="CD")] = -1
bmiData$A2[which (bmiData$A2=="MR")] = 1
bmiData$A2[which (bmiData$A2=="CD")] = -1
bmiData$A1 = as.numeric (bmiData$A1)
bmiData$A2 = as.numeric (bmiData$A2)
s1vars = bmiData[,1:4]
s2vars = bmiData[,c (1, 3, 5)]
a1 = bmiData[,7]
a2 = bmiData[,8]
## define response y to be the negative 12 month change in BMI from
## baseline 
y = -(bmiData[,6] - bmiData[,4])/bmiData[,4]
## second-stage regression
fitIQ2 = learnIQ2 (y ~ gender + parent_BMI + month4_BMI +
  A2*(parent_BMI + month4_BMI), data=bmiData, "A2", c("parent_BMI",
                                  "month4_BMI"))
## model conditional expected value of main effect term
fitIQ1main = learnIQ1main (~ gender + race + parent_BMI + baseline_BMI
  + A1*(gender + parent_BMI), data=bmiData, "A1", c ("gender",
                                "parent_BMI"), fitIQ2)
## model conditional mean of contrast function
fitIQ1cm = learnIQ1cm (~ gender + race + parent_BMI + baseline_BMI +
  A1*(gender + parent_BMI + baseline_BMI), data=bmiData, "A1", c
  ("gender", "parent_BMI", "baseline_BMI"), fitIQ2)
## variance modeling
fitIQ1var = learnIQ1var (fitIQ1cm) ## constant variance fit 
fitIQ1var = learnIQ1var (fitIQ1cm, s1vars, c (3, 4), method="hetero")
## non-constant variance fit
fitIQ1var = learnIQ1var (~ gender + race + parent_BMI + baseline_BMI +
	  A1*(parent_BMI), data=bmiData, "A1", c ("parent_BMI"),
	  "hetero", fitIQ1cm) 
## non-constant variance fit using formula specification  

iqLearn documentation built on May 2, 2019, 6:44 a.m.