R/ci.R2.R

In MBESS: The MBESS R Package

ci.R2 <- function(R2=NULL, df.1=NULL, df.2=NULL, conf.level=.95, Random.Predictors=TRUE, 
Random.Regressors, F.value=NULL, N=NULL, p=NULL, K, alpha.lower=NULL, alpha.upper=NULL, tol=1e-9)
{

# So that k or p can be specified.
tmp <- try(is.null(K), silent=TRUE)
if(tmp==TRUE | tmp==FALSE)
{

if(!is.null(p))
{
if(p != K) stop("Specificy 'p' or 'K', but not both (your 'p' and 'K' are different)")
}

p <- K
}


if(!missing(Random.Regressors)) Random.Predictors <- Random.Regressors

if((!is.null(N) | !is.null(p)) & (!is.null(df.1) | !is.null(df.2))) stop("Either specify \'df.1\' and \'df.2\' or \'N\' and \'p,\' but not both combinations.")

if(!is.null(N) & !is.null(p) & is.null(df.1) & is.null(df.2))
{
df.1 <- p
df.2 <- N-p-1
}

if(!is.null(df.1) & !is.null(df.2) & is.null(N) & is.null(p))
{
N <- df.1 + df.2 + 1
p <- df.1
}

if(!is.null(conf.level) & is.null(alpha.lower) & is.null(alpha.upper))
{
#if(conf.level >=1 | conf.level <= 0) stop("Your confidence level (\'conf.level\') must be between 0 and 1.")
if(!is.null(alpha.lower) | !is.null(alpha.upper)) stop("Since conf.level has been specified (which is done by default), you cannot specifiy \'alpha.lower\' and \'alpha.upper\'. If you want to specify \'alpha.lower\' or \'alpha.upper\', set \'conf.level=NULL\'")
alpha.lower <- alpha.upper <- (1-conf.level)/2
conf.level <- NULL
}

if(is.null(F.value))
{
F.value <- Rsquare2F(R2=R2, df.1=df.1, df.2=df.2, p=p, N=N)
}

if(is.null(R2))
{
R2 <- F2Rsquare(F.value=F.value, df.1=df.1, df.2=df.2)
}

if(Random.Predictors==FALSE)
{
Limits <- conf.limits.ncf(F.value=F.value, df.1=df.1, df.2=df.2, conf.level=NULL, tol=tol, alpha.lower=alpha.lower, alpha.upper=alpha.upper)

if(length(Limits)==4)
{
LL <- Lambda2Rsquare(Limits$Lower.Limit, N=N)
Prob.LL <- Limits$Prob.Less.Lower
UL <- Lambda2Rsquare(Limits$Upper.Limit, N=N)
Prob.UL <- Limits$Prob.Greater.Upper

if(is.na(Limits$Lower.Limit))
{
LL <- 0
Prob.LL <-0
}

if(is.na(Limits$Upper.Limit))
{
UL <- 1
Prob.UL <- 0
}

return(list(Lower.Conf.Limit.R2=LL, Prob.Less.Lower=Prob.LL, Upper.Conf.Limit.R2=UL, Prob.Greater.Upper=Prob.UL))
}

if(length(Limits)==2 & is.null(Limits$Upper.Limit))
{
return(list(Lower.Conf.Limit.R2=Lambda2Rsquare(Limits$Lower.Limit, N=N), Prob.Less.Lower=Limits$Prob.Less.Lower, Upper.Conf.Limit.R2=1, Prob.Greater.Upper=0))
}

if(length(Limits)==2 & is.null(Limits$Lower.Limit))
{
return(list(Lower.Conf.Limit.R2=0, Prob.Less.Lower=0, Upper.Conf.Limit.R2=Lambda2Rsquare(Limits$Upper.Limit, N=N), Prob.Greater.Upper=Limits$Prob.Greater.Upper))
}
}


if(Random.Predictors==TRUE)
{
pul <- alpha.upper
pll <- 1-alpha.lower

df1 <- N-1
df2 <- N-p-1

R2.Tilda <- R2/(1-R2)

x2 <- .999999
x1 <- .000001
x3 <- .5
diff3 <- 1

ulrhosq <- .5
llrhosq <- .5

if(pul!=0)
{
while((abs(diff3) > .00001) & (round(ulrhosq, 5) <1))
{
x3 <- (x1 + x2)/2
yy <- x3/(1-x3)
GAMMA <- sqrt(1+yy)
PHI.1 <- df1*(GAMMA^2 - 1) + p
PHI.2 <- df1*(GAMMA^4 - 1) + p
PHI.3 <- df1*(GAMMA^6 - 1) + p
g <- (PHI.2-sqrt(PHI.2^2 - PHI.1*PHI.3))/PHI.1
nu <- (PHI.2 - 2*yy*GAMMA*(sqrt(df1*df2)))/(g^2)
LAMBDA.U <- yy*GAMMA*(sqrt(df1*df2))/(g^2)
limit <- df2*R2.Tilda/(nu*g)
diff3 <- pf(limit, nu, df2, ncp=LAMBDA.U) - pul
yy <- x1/(1-x1)
GAMMA <- sqrt(1+yy)
PHI.1 <- df1*(GAMMA^2 - 1) + p
PHI.2 <- df1*(GAMMA^4 - 1) + p
PHI.3 <- df1*(GAMMA^6 - 1) + p
g <- (PHI.2-sqrt(PHI.2^2 - PHI.1*PHI.3))/PHI.1
nu <- (PHI.2 - 2*yy*GAMMA*(sqrt(df1*df2)))/(g^2)
LAMBDA.U <- yy*GAMMA*(sqrt(df1*df2))/(g^2)
limit <- df2*R2.Tilda/(nu*g)
diff1 <- pf(limit, nu, df2, ncp=LAMBDA.U) - pul
ifelse((diff1*diff3 < 0), (x2 <- x3), (x1 <- x3))
ulrhosq <- x3
}
}

###################################################

x2 <- .999999
x1 <- .000001
x3 <- .5

if(pll!=1)
{
yy <- x3/(1-x3)
GAMMA <- sqrt(1+yy)
PHI.1 <- df1*(GAMMA^2 - 1) + p
PHI.2 <- df1*(GAMMA^4 - 1) + p
PHI.3 <- df1*(GAMMA^6 - 1) + p
g <- (PHI.2-sqrt(PHI.2^2 - PHI.1*PHI.3))/PHI.1
nu <- (PHI.2 - 2*yy*GAMMA*(sqrt(df1*df2)))/(g^2)
LAMBDA.U <- yy*GAMMA*(sqrt(df1*df2))/(g^2)
limit <- df2*R2.Tilda/(nu*g)
diff3 <- pf(limit, nu, df2, ncp=LAMBDA.U) - pll

while((abs(diff3) > .00001) & (round(llrhosq, 5) < 1))
{
x3 <- (x1 + x2)/2
yy <- x3/(1-x3)
GAMMA <- sqrt(1+yy)
PHI.1 <- df1*(GAMMA^2 - 1) + p
PHI.2 <- df1*(GAMMA^4 - 1) + p
PHI.3 <- df1*(GAMMA^6 - 1) + p
g <- (PHI.2-sqrt(PHI.2^2 - PHI.1*PHI.3))/PHI.1
nu <- (PHI.2 - 2*yy*GAMMA*(sqrt(df1*df2)))/(g^2)
LAMBDA.U <- yy*GAMMA*(sqrt(df1*df2))/(g^2)
limit <- df2*R2.Tilda/(nu*g)
diff3 <- pf(limit, nu, df2, ncp=LAMBDA.U) - pll
yy <- x1/(1-x1)
GAMMA <- sqrt(1+yy)
PHI.1 <- df1*(GAMMA^2 - 1) + p
PHI.2 <- df1*(GAMMA^4 - 1) + p
PHI.3 <- df1*(GAMMA^6 - 1) + p
g <- (PHI.2-sqrt(PHI.2^2 - PHI.1*PHI.3))/PHI.1
nu <- (PHI.2 - 2*yy*GAMMA*(sqrt(df1*df2)))/(g^2)
LAMBDA.U <- yy*GAMMA*(sqrt(df1*df2))/(g^2)
limit <- df2*R2.Tilda/(nu*g)
diff1 <- pf(limit, nu, df2, ncp=LAMBDA.U) - pll
ifelse((diff1*diff3 < 0), (x2 <- x3), (x1 <- x3))
llrhosq <- x3
}
}

if(round(llrhosq, 5)==1 & llrhosq>R2) llrhosq <- 0

if(pll==1) llrhosq <- 0
if(pul==0) ulrhosq <- 1
if(llrhosq > ulrhosq) warning("There is a problem; the lower limit is greater than the upper limit (Are you at one of the boundries of Rho^2 or is alpha very large?).")

if(pll==1) return(list(Lower.Conf.Limit.R2=0, Prob.Less.Lower=0, Upper.Conf.Limit.R2=ulrhosq, Prob.Greater.Upper=pul))
if(pul==0) return(list(Lower.Conf.Limit.R2=llrhosq, Prob.Less.Lower=1-pll, Upper.Conf.Limit.R2=1, Prob.Greater.Upper=0))
return(list(Lower.Conf.Limit.R2=llrhosq, Prob.Less.Lower=1-pll, Upper.Conf.Limit.R2=ulrhosq, Prob.Greater.Upper=pul))
}
}