Tag Archive for ‘CI’ at RWebFriend 插件测试博客

The original blog article is "Confidence interval of R-square", but, which one?

Its R codes require package MBESS to calculate the confidence interval of $\rho^2$ for multiple regression, but visitors can't install packages on Rweb. The function source(...) of package base is the substitution. A source code file MBESS.ciR2.R including relevant functions in pacakge MBESS is uploaded online.

R2<-.68;    ###### Observed R-square            ######
N <- 150;   ###### Sample size                  ######
p <- 1;     ## Number of IV(s) other than intercept ##
conf.level=.95; ##  Confidence level            ######
## Only when p=1 , CI of R^2 can be calculated. ######
######################################################
##Input R-squared, Sample Size, number of IV(s),   ###
## and  confidence level                           ###
######################################################
## Usually you need not change the following codes ###
######################################################
## Output CIs of \eta^2, \rho^2, vs. R^2           ###
######################################################
##
source("http://ihome.cuhk.edu.hk/~s043115/data/MBESS.ciR2.R");
## substitute "require(MBESS)";
##
###############################
ci.eta2<-c((ci<-ci.R2(conf.level=conf.level,
R2=R2, N=N, p=p,
Random.Predictors=FALSE))$Lower.Conf.Limit.R2
,ci$Upper.Conf.Limit.R2);
ci.rho2<-c((ci<- ci.R2(conf.level=conf.level,
R2=R2, N=N, p=p,
Random.Predictors=TRUE))$Lower.Conf.Limit.R2
,ci$Upper.Conf.Limit.R2);
ci.R2 <- c((
max(0,
tanh(
atanh(sqrt(R2)) -
sqrt(2/(N-3))*qnorm(0.5+conf.level/2)
)
)
)^2 ,(
tanh(
atanh(sqrt(R2)) +
sqrt(2/(N-3))*qnorm(0.5+conf.level/2)
)
)^2);
(ci.R2);
if(p>1) ci.R2[] <- NA;
ci3<-data.frame(c(ci.eta2,ci.rho2,ci.R2)
,rep(c(' eta2',' rho2','Replicated R2'),each=2)
,c(rep(c('Lower','Upper'),3)));
names(ci3)<-c('CI','Type','Direction');
cat('<','h2><','font color=blue>',sep='');
tapply(ci3$CI,list(ci3$Type,ci3$Direction),mean);
cat('<','/font><','/h2>',sep='');
##to plot CI bars with boxplot
## let Q1,Q2,Q3 = R2 and Q0,Q4 as CI bounds
ci3.R2<-ci3;ci3.R2$CI[]<-R2;
plot(CI~Type,range=0,
data=rbind(ci3,ci3.R2,ci3.R2),xlab='',
ylab=paste(conf.level,'CI'),
main=paste('R2=',round(R2,4),', N=',N,'\n',p,' predictor(s) other than intercept'),
xlim=c(0,4),ylim=c(0,1));
abline(h=R2);

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