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R functions: EQ for MR.Rmd
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R functions: EQ for MR.Rmd
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---
title: "Thesis R Functions Udi Alter 2021"
author: "Udi Alter"
date: "30/04/2021"
---
```{r packages}
library(haven)
library(psych)
library(car)
library(psychometric)
library(QuantPsyc)
library(lsr)
library(apaTables)
library(dplyr)
library(broom)
```
# The *reg.equiv.fd* Function
### (when full data is available)
```{r reg.equiv.fd function}
reg.equiv.fd <- function(datfra, model, predictor, delta, alpha=.05, plot=TRUE, test="TOST", std=TRUE) {
# reg. coefficient point estimate and ci's
modres <- summary(model)
b.num <- grep(predictor, attr(model$terms , "term.labels"))+1 # this will indicate the place/number of the predictor in the model (e.g., 1st pred.) accounts for the intercept as well
b <- model$coefficients[b.num] # extract raw coefficient value
l.ci <- confint(model)[predictor,][1] # extract raw coefficient value, lower bound 95%
u.ci <- confint(model)[predictor,][2] # extract raw coefficient value, upper bound 95%
l.ci90 <- confint(model, level = .9)[predictor,][1] # extract raw coefficient value, lower bound 90%
u.ci90 <- confint(model, level = .9)[predictor,][2] # extract raw coefficient value, upper bound 90%
# std.error, degrees of freedom, and prerequisites
err <- modres$coefficients[b.num,2] # extract standard error for predictor
df <- model$df.residual # extract degrees of freedom for model
depname <- attr(model$terms, "variables")[[2]] # extract name of outcome variable
dep <- as.double(unlist(datfra[,depname])) # extract raw dependent variable values
pred <- as.double(unlist(datfra[,predictor])) # extract raw (tested) predictor variable values
#delta
l.delta <- -abs(delta) # lower equivalence interval bound (consider to make it as input in the function)
u.delta <- abs(delta) # upper equivalence interval bound
# standardized forms (beta, variables, delta, ci's)
beta <- data.frame(lm.beta(model))[predictor,] # extract standardized coefficient value
beta.err <- err*beta/b
dep.z <- (dep-mean(dep))/sd(dep) # constructing z scores for the dependent variable
pred.z <- (pred-mean(pred))/sd(pred) # constructing z scores for the predictor variable
std.delta <- delta*sd(pred)/sd(dep) # constructing a standardized form of delta
u.std.delta <- abs(std.delta) # standardized delta, upper
l.std.delta <- -abs(std.delta) # standardized delta, lower
l.std.ci <- (confint(model)[predictor,][1])*sd(pred)/sd(dep) # converting lower 95% ci to standardized form
u.std.ci <- (confint(model)[predictor,][2])*sd(pred)/sd(dep) # converting upper 95% ci to standardized form
l.std.ci90 <- (confint(model, level = .9)[predictor,][1])*sd(pred)/sd(dep) # converting lower 90% ci to standardized form
u.std.ci90 <- (confint(model, level = .9)[predictor,][2])*sd(pred)/sd(dep) # converting upper 90% ci to standardized form
# RESULTS SECTION
# standardized section
if (std==TRUE) {
std.delta <- delta
u.std.delta <- abs(std.delta)
l.std.delta <- -abs(std.delta)
raw.delta <- delta*sd(dep)/sd(pred)
u.raw.delta <- abs(raw.delta)
l.raw.delta <- -abs(raw.delta)
if (test=="AH") {
# AH
t.std.ah <- beta/beta.err
p.std.ah <- pt((abs(beta)-std.delta)/(sqrt(beta.err^2)),df) - pt((-abs(beta)-std.delta)/(sqrt(beta.err^2) ), df)
#cat("standardized regression coefficient for", predictor,":", "\n",
#"β = ",beta," , 95% CI [",l.std.ci,",",u.std.ci,"]" ,"\n",
#"associated std. error = ", beta.err, "\n", "\n",
#"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
#"\n",
#
cat("unstandardized regression coefficient for", predictor,":", "\n",
"b = ",b," , 95% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", err, "\n", "\n",
"standarized regression coefficient for", predictor,":","\n",
"β = ", beta,", 95% CI [",l.std.ci,",",u.std.ci,"]", "\n",
"associated std. error = ", beta.err, "\n", "\n",
"raw equivalence interval =","[",l.raw.delta,",",u.raw.delta,"]", "\n",
"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
"\n",
"Anderson-Hauck (AH) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t(",df,") = ",t.std.ah,"\n",
"p = ",p.std.ah,"\n",
ifelse(p.std.ah < alpha, "AH: Negligible effects concluded" , 'AH: Insufficient evidence for negligible effects'))
} else {
# TOST
t1.std.tost<- (beta-(-std.delta))/(sqrt(beta.err^2))
t2.std.tost<- (std.delta-beta)/(sqrt(beta.err^2))
p1.std.tost<- 1-pt(t1.std.tost, df)
p2.std.tost<- 1-pt(t2.std.tost, df)
#cat("standardized regression coefficient for", predictor,":", "\n",
#"β = ",beta," , 95% CI [",l.std.ci,",",u.std.ci,"]" ,"\n",
#"associated std. error = ", beta.err, "\n", "\n",
#"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
cat("unstandardized regression coefficient for", predictor,":", "\n",
"b = ",b," , 95% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", err, "\n", "\n",
"standarized regression coefficient for", predictor,":","\n",
"β = ", beta,", 95% CI [",l.std.ci,",",u.std.ci,"]", "\n",
"associated std. error = ", beta.err, "\n", "\n",
"raw equivalence interval =","[",l.raw.delta,",",u.raw.delta,"]", "\n",
"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
"\n",
"Two One-Sided Test (TOST) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t1(",df,") = ",t1.std.tost,"\n",
"t2(",df,") = ", t2.std.tost, "\n",
"p1 = ",p1.std.tost,"\n",
"p2 = ",p2.std.tost,"\n",
ifelse(p1.std.tost < alpha & p2.std.tost < alpha, 'TOST: Negligible effects concluded', 'TOST: Insufficient evidence for negligible effects'))
}
# plot
if (plot==TRUE) {
plot(NA, axes=F,
xlim = c(min(l.std.ci,l.std.delta)-max(u.std.ci-l.std.ci, u.std.delta-l.std.delta)/10, max(u.std.ci,u.std.delta)+max(u.std.ci-l.std.ci, u.std.delta-l.std.delta)/10),
ylim = c(0,1),
yaxt='n',
ylab="",
xlab = "Std. Regression Coefficient Estimate",
main = "Symmetric CI Approach \n 90% CI")
abline(v =0 , lty = 2, col= "light grey") # vertical line in the middle of the eq. interval, right now it's always 0, can be changed
points(x=beta, y=.5, pch=8, cex=2) # point at the estimated predictor value
abline(v=u.std.delta, lty=2, col = "red") # mark the upper eq. bound
abline(v=l.std.delta, lty=2, col = "red") # mark the lower eq. bound
segments(l.std.ci90,0.5,u.std.ci90,0.5, lwd=3) # plotting the 90% CI for the predictor estimate
text(u.std.delta*1.01,.5,"upper equivalence bound",srt=270,pos=3, offset = .5, col = "red") # text for eq. bound line (upper)
text(l.std.delta*1.01,.5,"lower equivalence bound",srt=90,pos=3, offset = .5, col = "red") # text for eq. bound line (lower)
text(u.std.delta*.9,-0.01,u.std.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (upper)
text(l.std.delta*0.88,-.01,l.std.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (lower)
text(beta,.57,round(beta, digits = 3),srt=0) # writing the predictor point estimate value
text(beta,.57,"β=",srt=0, pos = 2, offset = 1.5) # adding text to indicate above line
text(u.std.ci90,.45,round(u.std.ci90, digits = 3),pos =1, offset = .1, col = "black") # writing the 90% CI upper limit value for the predictor estimate
text(l.std.ci90,.45,round(l.std.ci90, digits = 3), pos =1, offset = .1,col = "black") # writing the 90% CI lower limit value for the predictor estimate
axis(side=1, pos=0, lwd.ticks=0)
}
} else {
# unstandardized section
if (test=="AH") {
# AH
t.ah <- modres$coefficients[b.num,3]
p.ah <- pt((abs(b)-delta)/(sqrt(err^2)),df) - pt((-abs(b)-delta)/(sqrt(err^2) ), df)
cat("unstandardized regression coefficient for", predictor,":", "\n",
"b = ",b," , 95% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", err, "\n", "\n",
"standarized regression coefficient for", predictor,":","\n",
"β = ", beta,", 95% CI [",l.std.ci,",",u.std.ci,"]", "\n", "\n",
"raw equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
"\n",
"Anderson-Hauck (AH) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t(",df,") = ",t.ah,"\n",
"p = ",p.ah,"\n",
ifelse(p.ah < alpha, "AH: Negligible effects concluded" , 'AH: Insufficient evidence for negligible effects'))
} else {
# TOST
t1.tost<- (b-(-delta))/(sqrt(err^2))
t2.tost<- (delta-b)/(sqrt(err^2))
p1.tost<- 1-pt(t1.tost, df)
p2.tost<- 1-pt(t2.tost, df)
cat("unstandardized regression coefficient for", predictor,":", "\n",
"b = ",b," , 95% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", err, "\n", "\n",
"standarized regression coefficient for", predictor,":","\n",
"β = ", beta,", 95% CI [",l.std.ci,",",u.std.ci,"]", "\n", "\n",
"raw equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"std. equivalence interval =","[",l.std.delta,",",u.std.delta,"]", "\n",
"\n",
"Two One-Sided Test (TOST) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t1(",df,") = ",t1.tost,"\n",
"t2(",df,") = ", t2.tost, "\n",
"p1 = ",p1.tost,"\n",
"p2 = ",p2.tost,"\n",
ifelse(p1.tost < alpha & p2.tost < alpha, 'TOST: Negligible effects concluded', 'TOST: Insufficient evidence for negligible effects'))
}
# plot
if (plot==TRUE) {
plot(NA, axes=F,
xlim = c(min(l.ci,l.delta)-max(u.ci-l.ci, u.delta-l.delta)/10, max(u.ci,u.delta)+max(u.ci-l.ci, u.delta-l.delta)/10),
ylim = c(0,1),
yaxt='n',
ylab="",
xlab = "Regression Coefficient Estimate",
main = "Symmetric CI Approach \n 90% CI")
abline(v =0 , lty = 2, col= "light grey") # vertical line in the middle of the eq. interval, right now it's always 0, can be changed
points(x=b, y=.5, pch=8, cex=2) # point at the estimated predictor value
abline(v=u.delta, lty=2, col = "red") # mark the upper eq. bound
abline(v=l.delta, lty=2, col = "red") # mark the lower eq. bound
segments(l.ci90,0.5,u.ci90,0.5, lwd=3) # plotting the 90% CI for the predictor estimate
text(u.delta*1.01,.5,"upper equivalence bound",srt=270,pos=3, offset = .5, col = "red") # text for eq. bound line (upper)
text(l.delta*1.01,.5,"lower equivalence bound",srt=90,pos=3, offset = .5, col = "red") # text for eq. bound line (lower)
text(u.delta*.9,-0.01,u.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (upper)
text(l.delta*0.88,-.01,l.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (lower)
text(b,.57,round(b, digits = 3),srt=0) # writing the predictor point estimate value
text(b,.57,"b=",srt=0, pos = 2, offset = 1.5) # adding text to indicate above line
text(u.ci90,.45,round(u.ci90, digits = 3),pos =1, offset = .1, col = "black") # writing the 90% CI upper limit value for the predictor estimate
text(l.ci90,.45,round(l.ci90, digits = 3), pos =1, offset = .1,col = "black") # writing the 90% CI lower limit value for the predictor estimate
axis(side=1, pos=0, lwd.ticks=0)
}
}
} # end of function
```
To use the function, fill in the missing input:
```{r using reg.equiv.fd}
reg.equiv.fd(datfra= , model= , predictor= , delta= , alpha=.05, plot=TRUE, test="TOST", std=TRUE)
```
# The *reg.equiv* Function
### (full data *not* necessary)
```{r reg.equiv function}
reg.equiv <- function(b, se, p, n, delta, alpha=.05, plot=TRUE, test="TOST", std=TRUE) {
# b = regression coefficient, std or raw
# se = std. error associated with the point estimate, b
# p = no. of predictors in the model
# n = sample size
# delta = SESOI, std or raw
df <- n-1-p
l.ci90 <- b+qt(.1/2,df, lower.tail = T)*se
u.ci90 <- b+qt(.1/2,df, lower.tail = F)*se
l.ci <- b+qt(alpha/2,df, lower.tail = T)*se
u.ci <- b+qt(alpha/2,df, lower.tail = F)*se
#delta
l.delta <- -abs(delta) # lower equivalence interval bound (consider to make it as input in the function)
u.delta <- abs(delta) # upper equivalence interval bound
# RESULTS SECTION
# standardized section
if (std==TRUE) {
if (test=="AH") {
# AH
t.ah <- b/se
p.ah <- pt((abs(b)-delta)/(sqrt(se^2)),df) - pt((-abs(b)-delta)/(sqrt(se^2) ), df)
cat("standardized regression coefficient is ","\n",
"β = ",b," ,", (1-alpha)*100, "% CI [",l.ci,",",u.ci,"]" ,"\n",
"associated std. error = ", se, "\n", "\n",
"std. equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"\n",
"Anderson-Hauck (AH) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t(",df,") = ",t.ah,"\n",
"p = ",p.ah,"\n",
ifelse(p.ah < alpha, "AH: Negligible effects concluded" , 'AH: Insufficient evidence for negligible effects'))
} else {
# TOST
t1.tost<- (b-(-delta))/(sqrt(se^2))
t2.tost<- (delta-b)/(sqrt(se^2))
p1.tost<- 1-pt(t1.tost, df)
p2.tost<- 1-pt(t2.tost, df)
cat("standardized regression coefficient is ","\n",
"β = ",b," ,", (1-alpha)*100, "% CI [",l.ci,",",u.ci,"]" ,"\n",
"associated std. error = ", se, "\n", "\n",
"std. equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"\n",
"Two One-Sided Test (TOST) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t1(",df,") = ",t1.tost,"\n",
"t2(",df,") = ", t2.tost, "\n",
"p1 = ",p1.tost,"\n",
"p2 = ",p2.tost,"\n",
ifelse(p1.tost < alpha & p2.tost < alpha, 'TOST: Negligible effects concluded', 'TOST: Insufficient evidence for negligible effects'))
}
# plot
if (plot==TRUE) {
plot(NA, axes=F,
xlim = c(min(l.ci,l.delta)-max(u.ci-l.ci, u.delta-l.delta)/10, max(u.ci,u.delta)+max(u.ci-l.ci, u.delta-l.delta)/10),
ylim = c(0,1),
yaxt='n',
ylab="",
xlab = "Std. Regression Coefficient Estimate",
main = "Symmetric CI Approach \n 90% CI")
abline(v =0 , lty = 2, col= "light grey") # vertical line in the middle of the eq. interval, right now it's always 0, can be changed
points(x=b, y=.5, pch=8, cex=2) # point at the estimated predictor value
abline(v=u.delta, lty=2, col = "red") # mark the upper eq. bound
abline(v=l.delta, lty=2, col = "red") # mark the lower eq. bound
segments(l.ci90,0.5,u.ci90,0.5, lwd=3) # plotting the 90% CI for the predictor estimate
text(u.delta*1.01,.5,"upper equivalence bound",srt=270,pos=3, offset = .5, col = "red") # text for eq. bound line (upper)
text(l.delta*1.01,.5,"lower equivalence bound",srt=90,pos=3, offset = .5, col = "red") # text for eq. bound line (lower)
text(u.delta*.9,-0.01,u.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (upper)
text(l.delta*0.88,-.01,l.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (lower)
text(b,.57,round(b, digits = 3),srt=0) # writing the predictor point estimate value
text(b,.57,"β=",srt=0, pos = 2, offset = 1.5) # adding text to indicate above line
text(u.ci90,.45,round(u.ci90, digits = 3),pos =1, offset = .1, col = "black") # writing the 90% CI upper limit value for the predictor estimate
text(l.ci90,.45,round(l.ci90, digits = 3), pos =1, offset = .1,col = "black") # writing the 90% CI lower limit value for the predictor estimate
axis(side=1, pos=0, lwd.ticks=0)
}
} else {
# unstandardized section
if (test=="AH") {
# AH
t.ah <- b/se
p.ah <- pt((abs(b)-delta)/(sqrt(se^2)),df) - pt((-abs(b)-delta)/(sqrt(se^2) ), df)
cat("unstandardized regression coefficient is ", "\n",
"b = ",b," ,", (1-alpha)*100, "% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", se, "\n", "\n",
"raw equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"\n",
"Anderson-Hauck (AH) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t(",df,") = ",t.ah,"\n",
"p = ",p.ah,"\n",
ifelse(p.ah < alpha, "AH: Negligible effects concluded" , 'AH: Insufficient evidence for negligible effects'))
} else {
# TOST
t1.tost<- (b-(-delta))/(sqrt(se^2))
t2.tost<- (delta-b)/(sqrt(se^2))
p1.tost<- 1-pt(t1.tost, df)
p2.tost<- 1-pt(t2.tost, df)
cat("unstandardized regression coefficient is ","\n",
"b = ",b," ,", (1-alpha)*100, "% CI [",l.ci,",",u.ci,"]" ,"\n",
"std. error = ", se, "\n", "\n",
"raw equivalence interval =","[",l.delta,",",u.delta,"]", "\n",
"\n",
"Two One-Sided Test (TOST) Equivalence Test Results:", "\n",
"-------------------------------------------------", "\n",
"t1(",df,") = ",t1.tost,"\n",
"t2(",df,") = ", t2.tost, "\n",
"p1 = ",p1.tost,"\n",
"p2 = ",p2.tost,"\n",
ifelse(p1.tost < alpha & p2.tost < alpha, 'TOST: Negligible effects concluded', 'TOST: Insufficient evidence for negligible effects'))
}
# plot
if (plot==TRUE) {
plot(NA, axes=F,
xlim = c(min(l.ci,l.delta)- max(u.ci-l.ci, u.delta-l.delta)/10, max(u.ci,u.delta)+max(u.ci-l.ci, u.delta-l.delta)/10),
ylim = c(0,1),
yaxt='n',
ylab="",
xlab = "Regression Coefficient Estimate",
main = "Symmetric CI Approach \n 90% CI")
abline(v =0 , lty = 2, col= "light grey") # vertical line in the middle of the eq. interval, right now it's always 0, can be changed
points(x=b, y=.5, pch=8, cex=2) # point at the estimated predictor value
abline(v=u.delta, lty=2, col = "red") # mark the upper eq. bound
abline(v=l.delta, lty=2, col = "red") # mark the lower eq. bound
segments(l.ci90,0.5,u.ci90,0.5, lwd=3) # plotting the 90% CI for the predictor estimate
text(u.delta*1.01,.5,"upper equivalence bound",srt=270,pos=3, offset = .5, col = "red") # text for eq. bound line (upper)
text(l.delta*1.01,.5,"lower equivalence bound",srt=90,pos=3, offset = .5, col = "red") # text for eq. bound line (lower)
text(u.delta*.9,-0.01,u.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (upper)
text(l.delta*0.88,-.01,l.delta,srt=0,pos=3, offset = .5, col = "red") # writing the eq. interval bound value (lower)
text(b,.57,round(b, digits = 3),srt=0) # writing the predictor point estimate value
text(b,.57,"b=",srt=0, pos = 2, offset = 1.5) # adding text to indicate above line
text(u.ci90,.45,round(u.ci90, digits = 3),pos =1, offset = .1, col = "black") # writing the 90% CI upper limit value for the predictor estimate
text(l.ci90,.45,round(l.ci90, digits = 3), pos =1, offset = .1,col = "black") # writing the 90% CI lower limit value for the predictor estimate
axis(side=1, pos=0, lwd.ticks=0)
}
}
} # end of function
```
To use the function, fill in the missing input:
```{r using reg.equiv}
reg.equiv(b= , se= , p= , n= , delta= , alpha=.05, plot=TRUE, test="TOST", std=TRUE)
```