forsearch_lm {forsearch}

Create Statistics Of Forward Search in a Linear Model Database

Description

Prepares summary statistics at each stage of forward search for subsequent plotting. Forward search is conducted in two steps: Step 1 to identify minimal set of observations to estimate unknown parameters, and Step 2 to add one observation at each stage such that observations in the set are best fitting at that stage.

Usage

forsearch_lm(formula, data, initial.sample=1000, n.obs.per.level = 1,
                   skip.step1 = NULL, unblinded = TRUE, begin.diagnose = 100,
                   verbose = TRUE)

Arguments

formula

Fixed effects formula as described in help(lm). The only permitted operators are +, : , and * . Terms must be found in data or as constructed by I(xxx) where xxx is found in data

data

Name of database

initial.sample

Number of observations in Step 1 of forward search

n.obs.per.level

Number of observations per level of (possibly crossed) factor levels.Set to rank of X'X if model contains constructed variables such as I(x^3), for example in polynomial regression

skip.step1

NULL or a vector of integers for observations to be included in Step 1

unblinded

TRUE causes printing of presumed analysis structure

begin.diagnose

Numeric. Indicates where in code to begin printing diagnostics. 0 prints all; 100 prints none

verbose

TRUE causes function identifier to display before and after run

Details

Step 2 is determined by the results of Step 1, which itself is random. So, it is possible to reproduce the entire run by using the skip.step1 argument.

Value

LIST

Rows in stage

Observation numbers of rows included at each stage

Standardized residuals

Matrix of errors at each stage

Number of model parameters

Rank of model

Sigma

Estimate of random error at final stage; used to standardize all residuals

Fixed parameter estimates

Vector of parameter estimates at each stage

s^2

Estimate of random error at each stage

Leverage

Matrix of leverage of each observation at each stage

Modified Cook distance

Estimate of sum of squared changes in parameter estimates at each stage

Call

Call to this function

Author(s)

William R. Fairweather

References

Atkinson, A and M Riani. Robust Diagnostic Regression Analysis, Springer, New York, 2000.

Examples

# Multiple regression
Observation <- 1:16
y <- runif(16)
x1 <- runif(16)
x2 <- runif(16)
x3 <- runif(16)
lmtest1 <- data.frame(Observation,y,x1,x2,x3)
forsearch_lm(formula=y~x1+x2+x3, data=lmtest1, initial.sample=200,begin.diagnose=100)
## Not run: 

# Analysis of variance 
Observation <- 1:30
y <- runif(30)
AN1 <- as.factor(c(rep("A1",5),rep("A2",5),rep("A3",5)))
AN1 <- c(AN1,AN1)
AN2 <- as.factor(c(rep("B1",15),rep("B2",15)))
lmtest2 <- data.frame(Observation,y,AN1,AN2)
forsearch_lm(formula=y~AN1*AN2, data=lmtest2, initial.sample=200,begin.diagnose=100)

# Analysis of covariance
Observation <- 1:60
y <- runif(60)
AN1 <- as.factor(c(rep("A1",10),rep("A2",10),rep("A3",10)))
AN1 <- c(AN1,AN1)
AN2 <- as.factor(c(rep("B1",30),rep("B2",30)))
COV <- runif(60)
lmtest3 <- data.frame(Observation,y,AN1,AN2,COV)
forsearch_lm(formula=y~AN1*AN2+COV, data=lmtest3, initial.sample=200,begin.diagnose=100)

# Polynomial regression
C1 <- 7*runif(60) + 1
y <- 4 + C1 - 6*C1^2 + 9*C1^3 + rnorm(60)
Observation <- 1:60
dfpoly <- data.frame(Observation,C1,y) 
forsearch_lm(formula = y ~ C1 + I(C1^2) + I(C1^3), data = dfpoly,  initial.sample = 200, 
     begin.diagnose=100)

## End(Not run)