Cohen's Kappa for 2 raters

Description

Computes Cohen's Kappa for agreement in the case of 2 raters. The diagnosis (the object of the rating) may have k possible values.

Usage

ckappa(r)

Arguments

Details

The function deals with the case where the two raters have not exactly the same scope of rating (some software associate an error with this situation). Missing value are omitted.

Value

A list with :

Author(s)

Bruno Falissard

References

Cohen, J. (1960), A coefficient of agreement for nominal scales, Educational and Psychological measurements, 20, 37-46.

Examples

data(expsy)
## Cohen's kappa for binary diagnosis
ckappa(expsy[,c(12,14)])

##to obtain a 95%confidence interval:
#library(boot)
#ckappa.boot <- function(data,x) {ckappa(data[x,])[[2]]}
#res <- boot(expsy[,c(12,14)],ckappa.boot,1000)
## two-sided bootstrapped confidence interval of kappa
#quantile(res$t,c(0.025,0.975))
## adjusted bootstrap percentile (BCa) confidence interval (better)
#boot.ci(res,type="bca")
##Cohen's kappa for non binary diagnosis
#ckappa(expsy[,c(11,13)])

Cronbach's coefficient alpha

Description

Computes the Cronbach's reliability coefficient alpha. This coefficient may be applied to a series of items destinated to be aggregated in a single score. It estimates reliability in the framework of the domain sampling model.

Usage

cronbach(v1)

Arguments

Details

Missing value are omitted in a "listwise" way (all items are removed even if only one of them is missing).

Value

A list with :

Author(s)

Bruno Falissard

References

Nunnaly, J.C., Bernstein, I.H. (1994), Psychometric Theory, 3rd edition, McGraw-Hill Series in Psychology.

Examples

data(expsy)
cronbach(expsy[,1:10])  ## not good because item 2 is reversed (1 is high and 4 is low)
cronbach(cbind(expsy[,c(1,3:10)],-1*expsy[,2]))  ## better

#to obtain a 95%confidence interval:
#datafile <- cbind(expsy[,c(1,3:10)],-1*expsy[,2])
#library(boot)
#cronbach.boot <- function(data,x) {cronbach(data[x,])[[3]]}
#res <- boot(datafile,cronbach.boot,1000)
#quantile(res$t,c(0.025,0.975))  ## two-sided bootstrapped confidence interval of Cronbach's alpha
#boot.ci(res,type="bca")         ## adjusted bootstrap percentile (BCa) confidence interval (better)

Depressive Mood Scale

Description

A data frame with 269 observations on the following 20 variables. Jouvent, R et al 1988 La clinique polydimensionnelle de humeur depressive. Nouvelle version echelle EHD : Polydimensional rating scale of depressive mood. Psychiatrie et Psychobiologie.

Usage

data(ehd)

Format

This data frame contains the following columns:

e1

Observed painfull sadness

e2

Emotional hyperexpressiveness

e3

Emotional instability

e4

Observed monotony

e5

Lack spontaneous expressivity

e6

Lack affective reactivity

e7

Emotional incontinence

e8

Affective hyperesthesia

e9

Observed explosive mood

e10

Worried gesture

e11

Observed anhedonia

e12

Felt sadness

e13

Situational anhedonia

e14

Felt affective indifference

e15

Hypersensibility unpleasent events

e16

Sensory anhedonia

e17

Felt affective monotony

e18

Felt hyperemotionalism

e19

Felt irritability

e20

Felt explosive mood

Source

Jouvent, R et al 1988 La clinique polydimensionnelle de humeur depressive. Nouvelle version echelle EHD : Polydimensional rating scale of depressive mood. Psychiatrie et Psychobiologie.

Examples

data(ehd)
str(ehd)

Data set related to psychometry

Description

The expsy data frame has 30 rows and 16 columns with missing data. it1-it10 correspond to the rating of 30 patients with a 10 items scale. r1, r2, r3 to the rating of item 1 by 3 different clinicians of the same 30 patients. rb1, rb2, rb3 to the binary transformation of r1, r2, r3 (1 or 2 -> 0; and 3 or 4 -> 1) .

Usage

data(expsy)

Format

This data frame contains the following columns:

it1

a numeric vector corresponding to item 1 (rated from 1:low to 4:high)

it2

a numeric vector corresponding to item 2 (rated from 1:high to 4:low)

it3

a numeric vector corresponding to item 3 (rated from 1:low to 4:high)

it4

a numeric vector corresponding to item 4 (rated from 1:low to 4:high)

it5

a numeric vector corresponding to item 5 (rated from 1:low to 4:high)

it6

a numeric vector corresponding to item 6 (rated from 1:low to 4:high)

it7

a numeric vector corresponding to item 7 (rated from 1:low to 4:high)

it8

a numeric vector corresponding to item 8 (rated from 1:low to 4:high)

it9

a numeric vector corresponding to item 9 (rated from 1:low to 4:high)

it10

a numeric vector corresponding to item 10 (rated from 1:low to 4:high)

r1

a numeric vector corresponding to item 1 rated by rater 1

rb1

binary transformation of r1

r2

a numeric vector corresponding to item 1 rated by rater 2

rb2

binary transformation of r2

r3

a numeric vector corresponding to item 1 rated by rater 3

rb3

binary transformation of r3

Source

artificial data

Examples

data(expsy)
expsy[1:4,]

Focused Principal Components Analysis

Description

Graphical representation similar to a principal components analysis but adapted to data structured with dependent/independent variables

Usage

fpca(formula=NULL,y=NULL, x=NULL, data, cx=0.75, pvalues="No",
     partial="Yes", input="data", contraction="No", sample.size=1)

Arguments

Details

This representation is close to a Principal Components Analysis (PCA). Contrary to PCA, correlations between the dependent variable and the other variables are represented faithfully. The relationships between non dependent variables are interpreted like in a PCA: correlated variables are close or diametrically opposite (for negative correlations), independent variables make a right angle with the origin. The focus on the dependent variable leads formally to a partialisation of the correlations between the non dependent variables by the dependent variable (see reference). To avoid this partialisation, the option partial="No" can be used. It may be interesting to represent graphically the strength of association between the dependent variable and the other variables using p values coming from a model. A vector of pvalue may be specified in this case.

Value

A plot (q plots in fact).

Author(s)

Bruno Falissard, Bill Morphey, Adeline Abbe

References

Falissard B, Focused Principal Components Analysis: looking at a correlation matrix with a particular interest in a given variable. Journal of Computational and Graphical Statistics (1999), 8(4): 906-912.

Examples

data(sleep)
fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+
     Gestation.time+Predation+Sleep.exposure+Danger,data=sleep)
fpca(y="Paradoxical.sleep",x=c("Body.weight","Brain.weight","Slow.wave.sleep",
     "Maximum.life.span","Gestation.time","Predation","Sleep.exposure","Danger"),data=sleep)


## focused PCA of the duration of paradoxical sleep (dreams, 5th column)
## against constitutional variables in mammals (columns 2, 3, 4, 7, 8, 9, 10, 11).
## Variables inside the red cercle are significantly correlated
## to the dependent variable with p<0.05.
## Green variables are positively correlated to the dependent variable,
## yellow variables are negatively correlated.
## There are three clear clusters of independent variables.

corsleep <- as.data.frame(cor(sleep[,2:11],use="pairwise.complete.obs"))
fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+
    Gestation.time+Predation+Sleep.exposure+Danger,
data=corsleep,input="Cor",sample.size=60)

## when missing data are numerous, the representation of a pairwise correlation
## matrix may be preferred (even if mathematical properties are not so good...)

numer <- c(2:4,7:11)
l <- length(numer)
resu <- vector(length=l)
for(i in 1:l)
{
int <- sleep[,numer[i]]
mod <- lm(sleep$Paradoxical.sleep~int)
resu[i] <-  summary(mod)[[4]][2,4]*sign(summary(mod)[[4]][2,1])
}
fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+
     Gestation.time+Predation+Sleep.exposure+Danger,
data=sleep,pvalues=resu)
## A representation with p values
## When input="Cor" or pvalues="Yes" partial is turned to "No"

mod <- lm(sleep$Paradoxical.sleep~sleep$Body.weight+sleep$Brain.weight+
sleep$Slow.wave.sleep+sleep$Maximum.life.span+sleep$Gestation.time+
sleep$Predation+sleep$Sleep.exposure+sleep$Danger)
resu <-  summary(mod)[[4]][2:9,4]*sign(summary(mod)[[4]][2:9,1])
fpca(Paradoxical.sleep~Body.weight+Brain.weight+Slow.wave.sleep+Maximum.life.span+
     Gestation.time+Predation+Sleep.exposure+Danger,
data=sleep,pvalues=resu)
## A representation with p values which come from a multiple linear model
## (here results are difficult to interpret)

Intraclass correlation coefficient (ICC)

Description

Computes the ICC of several series of measurements, for example in an interrater agreement study. Two types of ICC are proposed: consistency and agreement.

Usage

icc(data)

Arguments

Details

Missing data are omitted in a listwise way. The "agreement" ICC is the ratio of the subject variance by the sum of the subject variance, the rater variance and the residual; it is generally prefered. The "consistency" version is the ratio of the subject variance by the sum of the subject variance and the residual; it may be of interest when estimating the reliability of pre/post variations in measurements.

Value

A list with :

Author(s)

Bruno Falissard

References

Shrout, P.E., Fleiss, J.L. (1979), Intraclass correlation: uses in assessing rater reliability, Psychological Bulletin, 86, 420-428.

Examples

data(expsy)
icc(expsy[,c(12,14,16)])

#to obtain a 95%confidence interval:
#library(boot)
#icc.boot <- function(data,x) {icc(data[x,])[[7]]}
#res <- boot(expsy[,c(12,14,16)],icc.boot,1000)
#quantile(res$t,c(0.025,0.975))  # two-sided bootstrapped confidence interval of icc (agreement)
#boot.ci(res,type="bca")         # adjusted bootstrap percentile (BCa) confidence interval (better)

Light's kappa for n raters

Description

Computes Light's Kappa for agreement in the case of n raters. The diagnosis (the object of the rating) may have k possible values (ordered or not).

Usage

lkappa(r, type="Cohen", weights="squared")

Arguments

Details

Light's Kappa is equal to the mean of the n(n-1)/2 kappas obtained from each pair of raters. Missing values are omitted locally when considering each pair of raters. If type="Cohen" the diagnosis is considered as a categorical variable. If not, the diagnosis is considered as an ordered variable and weigthed kappa's are computed. In this last situation, the type of weights that is used (squared or absolute values) is given by the variable weigths.

Value

kappa (mean of the n(n-1)/2 kappas obtained from each pair of raters)

Author(s)

Bruno Falissard

References

Conger, A.J. (1980), Integration and generalisation of Kappas for multiple raters, Psychological Bulletin, 88, 322-328.

Examples

data(expsy)
lkappa(expsy[,c(11,13,15)])       # Light's kappa for non binary diagnosis
lkappa(expsy[,c(12,14,16)])       # Light's kappa for binary diagnosis
lkappa(expsy[,c(11,13,15)], type="weighted")      # Light's kappa for non binary ordered diagnosis

#to obtain a 95%confidence interval:
#library(boot)
#lkappa.boot <- function(data,x) {lkappa(data[x,], type="weighted")}
#res <- boot(expsy[,c(11,13,15)],lkappa.boot,1000)
#quantile(res$t,c(0.025,0.975))    # Bootstrapped confidence interval of Light's kappa
#boot.ci(res,type="bca")           # adjusted bootstrap percentile (BCa) confidence interval

Graphical representation of a correlation matrix using a Principal Component Analysis

Description

Similar to many routines, the interest is in the possible representation of both variables and subjects (and by the way categorical variables) with active and supplementary points. Missing data are omitted.

Usage

mdspca(datafile, supvar="no", supsubj="no", namesupvar=colnames(supvar,do.NULL=FALSE),
       namesupsubj=colnames(supsubj, do.NULL=FALSE), dimx=1, dimy=2, cx=0.75)

Arguments

Value

A diagram (two diagrams if supplementary subjects are used)

Author(s)

Bruno Falissard

Examples

data(sleep)

mdspca(sleep[,c(2:5,7:11)])
## three consistent groups of variables, paradoxical sleep (in other words: dream)
## is negatively correlated with danger

mdspca(sleep[,c(2:5,7:11)],supvar=sleep[,6],namesupvar="Total.sleep",supsubj=sleep[,1],
       namesupsubj="",cx=0.5)
## Total.sleep is here a supplementary variable since it is deduced
## from Paradoxical.sleep and Slow.wave.sleep
## The variable Species is displayed in the subject plane,
## Rabbit and Cow have a high level of danger

Multitrait Multimethod approach of scale validation

Description

This function is destinated to assess the convergent and discriminant validity of subscales of a given scale. Items belonging to the same subscale should correlate highly amongst themselves. Items belonging to different subscales should not correlate highly. This approach is simpler and more robust than confirmatory factor analysis (CFA). It can be interesting to verify (at least approximately) the proposed structure of an existing instrument in a new population. Most psychometricians will however prefer CFA.

Usage

mtmm(datafile,x,color=FALSE,itemTot=FALSE,graphItem=FALSE,stripChart=FALSE,namesDim=NULL)
 

Arguments

Value

For subscale i (i=1,...,n), displays the n boxplots of the distributions of the Pearson's correlations between items of subscale i and items of subscale j (j=1,...,n). If j=i, the correlation of a given item with itself is ommited. Boxplot for i=j (grey by default) should be above boxplots for i!=j. Likewise, the correlation of an item with the global score of its subscale should be above its correlations with the global score of the other subscales.

Author(s)

Adeline Abbe

Examples

data(ehd)

par(mfrow=c(1,5))
mtmm(ehd,list(c("e15","e18","e19","e20"),c("e4","e5","e6","e14","e17"),c("e11","e13","e16")
,c("e1","e10","e12"),c("e2","e3","e7","e8","e9")))

# Boxplots of the distributions of the Pearson's correlations between total score of
# subscale i and the items of subscale j
par(mfrow=c(1,5))
mtmm(ehd,list(c("e15","e18","e19","e20"),c("e4","e5","e6","e14","e17"),c("e11","e13","e16")
,c("e1","e10","e12"),c("e2","e3","e7","e8","e9")))

# Pearson's correlations between total score of subscale i and all items
par(mfrow=c(3,2))
mtmm(ehd,list(c("e15","e18","e19","e20"),c("e4","e5","e6","e14","e17"),c("e11","e13","e16")
,c("e1","e10","e12"),c("e2","e3","e7","e8","e9")),graphItem=TRUE)

Various procedures used in psychometry

Description

Kappa, Intra class correlation coefficient, Cronbach alpha, Scree plot, Multitraits multimethods, Spherical representation of a correlation matrix

Details

Author(s)

Bruno Falissard <falissard_b@wanadoo.fr>

References

Falissard B, A spherical representation of a correlation matrix, Journal of Classification (1996), 13:2, 267-280.
Horn, JL (1965) A Rationale and Test for the Number of Factors in Factor Analysis, Psychometrika, 30, 179-185.
Mammals: Ecological and Constitutional Correlates, by Allison, T. and Cicchetti, D. (1976) Science, November 12, vol. 194, pp.732-734
Jouvent, R et al 1988 La clinique polydimensionnelle de humeur depressive. Nouvelle version echelle EHD : Polydimensional rating scale of depressive mood. Psychiatrie et Psychobiologie.

Examples

data(sleep)
sphpca(sleep[,c(2:5,7:11)])
data(expsy)
scree.plot(expsy[,1:10],simu=20,use="P")
data(ehd)
par(mfrow=c(1,5))
mtmm(ehd,list(c("e15","e18","e19","e20"),c("e4","e5","e6","e14","e17"),c("e11","e13","e16")
,c("e1","e10","e12"),c("e2","e3","e7","e8","e9")))

Screeplot of eigenvalues, simulated data are available

Description

Graphical representation of the eigenvalues of a correlation/covariance matrix. Usefull to determine the dimensional structure of a set of variables. Simulation are proposed to help the interpretation.

Usage

scree.plot(namefile, title = "Scree Plot", type = "R", use = "complete.obs", simu = "F")

Arguments

Details

Simulations lead sometimes to underestimate the actual number of dimensions (as opposed to Kayser rule: eigen values superior to 1). Basically, simu=20 is enough.

Value

a plot

Author(s)

Bruno Falissard

References

Horn, JL (1965) A Rationale and Test for the Number of Factors in Factor Analysis, Psychometrika, 30, 179-185. Cattell, RB (1966) The scree test for the number of factors. Multivariate Behavioral Research, 1, 245-276.

Examples

data(expsy)
scree.plot(expsy[,1:10],simu=20,use="P") #no obvious structure with such a small sample

Ecological and Constitutional Data in Mammals

Description

Data from which conclusions were drawn in the article Mammals: Ecological and Constitutional Correlates, by Allison, T. and Cicchetti, D. (1976) Science, November 12, vol. 194, pp.732-734

Usage

data(sleep)

Format

This data frame contains the following columns:

Species

a factor with levels

Body.weight

a numeric vector, body weight in kg

Brain.weight

a numeric vector, Brain weight in g

Slow.wave.sleep

a numeric vector, nondreaming sleep (hrs/day)

Paradoxical.sleep

a numeric vector, dreaming sleep (hrs/day)

Total.sleep

a numeric vector, nondreaming + "dreaming" (hrs/day)

Maximum.life.span

a numeric vector (in years)

Gestation.time

a numeric vector (in days)

Predation

a numeric vector, Predation index (1 min - 5 max)

Sleep.exposure

a numeric vector, Sleep exposure index (1 min - 5 max)

Danger

a numeric vector, Overall danger index (1 min - 5 max)

Source

http://lib.stat.cmu.edu/datasets/sleep

References

Mammals: Ecological and Constitutional Correlates, by Allison, T. and Cicchetti, D. (1976) Science, November 12, vol. 194, pp.732-734

Examples

data(sleep)
str(sleep)

Spherical Representation of a Correlation Matrix

Description

Graphical representation of a correlation matrix, similar to principal component analysis (PCA) but the mapping is on a sphere. The information is close to a 3d PCA, the picture is however easier to interpret since the variables are in fact on a 2d map.

Usage

sphpca(datafile, h=0, v=0, f=0, cx=0.75, nbsphere=2, back=FALSE, input="data",
       method="approx", maxiter=500, output=FALSE)

Arguments

Details

There is an isophormism between a correlation matrix and points on the unit hypersphere of Rn. It can be shown that a 3d spherical representation of a correlation matrix is statistically and cognitively interesting (see reference). The default option method="approx" is based on a principal components approximation (see reference). It is fast and gives rather good results. If method="exact" the representation is sligthly improved in terms of fit (the sphere minimizes the sum of squared distances between the original variables on the hypersphere and their projections on the sphere). The option method="rscal" optimizes the representation of correlations between variables with distances between points (in a least squares sense). For convenience, the scaling of points on the sphere is chosen so that angles between points are linearly related to correlations between variables (this is not the case on the hypersphere were d=[2*(1-r)]^0.5). For method="exact" or method="rscal" computations may be rather lengthy (and not sensible for more than 20-40 variables). The sphere may be rotated to help in visualising most of variables on a same side (front for example). By default, the back of the sphere (right plot) is not seen showing through.

Value

A plot. If method="rscal" and output=TRUE, a list with :

Author(s)

Bruno Falissard

References

Falissard B, A spherical representation of a correlation matrix, Journal of Classification (1996), 13:2, 267-280.

Examples

data(sleep)
sphpca(sleep[,c(2:5,7:11)])
## spherical representation of ecological and constitutional correlates in mammals

sphpca(sleep[,c(2:5,7:11)],method="rscal",output=TRUE)
## idem, but optimizes the representation of correlations between variables with distances
## between points

corsleep <- as.data.frame(cor(sleep[,c(2:5,7:11)],use="pairwise.complete.obs"))
sphpca(corsleep,input="Cor")
sphpca(corsleep,method="rscal",input="Cor")
## when missing data are numerous, the representation of a pairwise correlation
## matrix may be preferred (even if mathematical properties are not so good...)

sphpca(corsleep,method="rscal",input="Cor",h=180,f=180,nbsphere=1,back=TRUE)
## other option of presentation

##
# library(polycor)
# sleep$Predation <- as.ordered(sleep$Predation)
# sleep$Sleep.exposure <- as.ordered(sleep$Sleep.exposure)
# sleep$Danger <- as.ordered(sleep$Danger)
# corsleeph <- as.data.frame(hetcor(sleep[,c(2:5,7:11)])$correlations)
# sphpca(corsleeph,input="Cor",f=180)
# sphpca(corsleeph,method="rscal",input="Cor",f=180)
## --> Correlations between discrete variables may appear shoking to some statisticians (?)
## --> Representation of polychoric/polyserial correlations could be prefered in this situation

weighted Kappa for 2 raters

Description

Computes a weighted Kappa for agreement in the case of 2 raters. The diagnosis (the object of the rating) may have k possible ordered values.

Usage

wkappa(r,weights="squared")

Arguments

Details

Diagnoses have to be coded by numbers (ordered naturally). For weigths="squared", weights are related to squared differences between rows and columns indices (in this situation wkappa is close to an icc). For weights!="squared", weights are related to absolute values of differences between rows and columns indices. The function is supposed to deal with the case where the two raters have not exactly the same scope of rating. Missing value are omitted.

Value

A list with :

Author(s)

Bruno Falissard

References

Cohen, J. Weighted kappa: nominal scale agreement with provision for scaled disagreement or partial credit. Psychological Bulletin 70 (1968): 213-220.

Examples

data(expsy)
wkappa(expsy[,c(11,13)])        # weighted kappa (squared weights)

#to obtain a 95%confidence interval:
#library(boot)
#wkappa.boot <- function(data,x) {wkappa(data[x,])[[3]]}
#res <- boot(expsy[,c(11,13)],wkappa.boot,1000)
#quantile(res$t,c(0.025,0.975))  # two-sided bootstrapped confidence interval of weighted kappa
#boot.ci(res,type="bca")         # adjusted bootstrap percentile (BCa) confidence interval (better)