| Title: | Calculates a generalized discriminant function to unmix two classes, typically sexes of birds |
|---|---|
| Description: | The goal of Gendis2unmix is to sex birds from a population on the basis of several measurements. The key feature is that the birds from different populations may differ in size but that within populations females are smaller than males (or reversely). The predict function for a set of unsexed birds from a new population therefore estimates a new cutoff value which thus depends on the sizes of the birds in the new population. In the training phase, a generalized discriminant function (GDF) is calculated from a birds of known sex of different populations, in which the algorithm uses a common within-covariance matrix across populations and sexes. In the prediction phase Gendis2unmix then applies the GDF to measurements of individuals of unknow sex or class. The cutoff value is determined by unmixing the distribution in terms of two normal distributions with unequal means and variances using an EM algorithm. The parametric approach taken in Gendis2unmix make it suitable for small number of samples in both the training and prediction phase (say 20-100 per sex/population). |
| Authors: | Cajo J.F. ter Braak |
| Maintainer: | Cajo J.F. ter Braak <[email protected]> |
| License: | GPL-3 | file LICENSE |
| Version: | 0.1.1 |
| Built: | 2024-11-21 04:49:30 UTC |
| Source: | https://github.com/CajoterBraak/Gendis2unmix |
The dataframe fulmarin contains measurements on Fulmarine petrels
with sex known from dissection or, for Snow Petrels, observation. The variables are as follows:
population study site ID (integer)
1 Northern Fulmar (Fulmarus glacialis), the Netherlands
2 Northern Fulmar (Fulmarus glacialis), Jan Mayen
3 Southern Fulmar (Fulmarus glacialoides), Ardery Island Antarctica
4 Cape Petrel (Daption capense), Ardery Island Antarctica
5 Antarctic Petrel (Thalassoica antarctica), Ardery Island, Antarctica
6 Snow Petrel (Pagodroma nivea), Casey Station, Antarctica
sex 0 is female; 1 is male
HB Head Length (mm)
BD2 Bill Depth at gonys (mm)
TL Tarsus Length (mm)
CL Culmen Length (mm).
Jan Andries van Franeker ([email protected])
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502, https://doi.org/10.2307/4088413 https://edepot.wur.nl/249350
gendis calculates a generalized discriminant function to distinguish two classes,
typically sexes (male and female birds)
based on measurements of a number of indicators for individuals from each of the two sexes
from a series of different populations in which individuals may have a different mean size but
a common-within covariance matrix.
gendis( population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE, data )gendis( population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE, data )
population |
a name of the variable for the populations in the data (default "population") |
sex |
a name of the variable indicating the two classes to distinguish in the data (default "sex") (0 vs 1 or "female" vs "male") |
measurements |
character ("other_variables", default) or character vector with names of
measurement variables. |
verbose |
logical (default = FALSE) |
data |
data frame with variables |
An object of class gendis which is a named list, among which,
population |
name of variable indicating populations |
sex |
name of variable indicating the two sexes or classes |
classnames |
names for the classes of sex (level or value) |
measurements |
names of the variables in the GDF |
GDF |
the Generalized Discriminant Function, matrix with two columns differing in scaling of the GDF |
mean.male |
overall mean of males (the second level of factor(sex)) |
mean.female |
overall mean of females (the first level of factor(sex)) |
within.sd |
overall within standard deviation |
cov_overall |
overall within-group covariance matrix |
means.male |
mean of males per population |
means.female |
mean of females per population |
within.sds |
within standard deviation per population |
ind_mv |
number of males and females per population |
cov_list |
within-group covariance matrix per population |
Nind |
number of individuals |
Np |
number of populations |
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502, https://doi.org/10.2307/4088413 https://edepot.wur.nl/249350
predict.gendis, summary.gendis, print.gendis.
data("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDFdata("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDF
The data frame JanMayenBirds contains measurements on the Northern Fulmar petrels birds from
the population at Jan Mayen.
From the first 32 birds the sex is known by dissection, from the remaining 162 birds the sex is unknown.
JAFCODE bird code (character)
LOCATION location (character)
DATE measurement date (character)
DISSEX 0 is female; 1 is male
HB Head Length (mm)
BD2 Bill Depth at gonys (mm)
TL Tarsus Length (mm)
CL Culmen Length (mm.
Jan Andries van Franeker ([email protected])
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502, https://doi.org/10.2307/4088413 https://edepot.wur.nl/249350
predict.gendis applies a generalized discriminant function created with gendis
to predict the sex (class) of each individual with measurements in newdata. From the gendis
object, the coefficients that define the generalized discriminant function (GDF) are applied to the
newdata to obtain the discriminant scores.
## S3 method for class 'gendis' predict(object, newdata, type = object$sex, verbose = FALSE, ...)## S3 method for class 'gendis' predict(object, newdata, type = object$sex, verbose = FALSE, ...)
object |
an object of class gendis, typically created with |
newdata |
a data frame with measurements on (new) individuals with variables used to create |
type |
what to predict: the sex or class of each individual (default),
the generalized discriminant scores with cutpoint ("GDF" or "GDFscore") or
the full output of the unmixing algorithm |
verbose |
logical (default = FALSE). If TRUE a plot of the density of the GDF is produced. |
... |
other optional arguments |
The discriminant score are a linear combination of the variables in newdata
that are shared with the variables used to create the object. The linear combination is defined by
the GDF coefficients. The discriminant scores are subjected to an unmixing algorithm. This algorithm (unmix) generates a cutpoint
below which individuals are predicted to be female (level 1 of factor(sex)) and above which they are predicted to be
male (level 2 of factor(sex)). The cutpoint is at the point of intersection of two normal densities with unequal
means and variances fitted to the discriminant scores (see unmix for details).
See argument type.
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502, https://doi.org/10.2307/4088413 https://edepot.wur.nl/249350
data("fulmarin") str(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) data("JanMayenBirds") sex.predict <- predict(result, newdata = JanMayenBirds, verbose = TRUE) # one false prediction: (number 32) data.frame(sex = JanMayenBirds$DISSEX, sex.predict)[seq(from=2, to = 37, by =5),] predict(result, JanMayenBirds ) # same as default above predict(result, JanMayenBirds, type = result$sex, verbose = FALSE) # GDF score with cutpoint predict(result, JanMayenBirds, type = "GDF", verbose = FALSE) # unmix results only predict(result, JanMayenBirds, type = "cutpoint", verbose = TRUE)data("fulmarin") str(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) data("JanMayenBirds") sex.predict <- predict(result, newdata = JanMayenBirds, verbose = TRUE) # one false prediction: (number 32) data.frame(sex = JanMayenBirds$DISSEX, sex.predict)[seq(from=2, to = 37, by =5),] predict(result, JanMayenBirds ) # same as default above predict(result, JanMayenBirds, type = result$sex, verbose = FALSE) # GDF score with cutpoint predict(result, JanMayenBirds, type = "GDF", verbose = FALSE) # unmix results only predict(result, JanMayenBirds, type = "cutpoint", verbose = TRUE)
print.gendis prints the results of gendis in more detail than summary.gendis.
## S3 method for class 'gendis' print(x, ...)## S3 method for class 'gendis' print(x, ...)
x |
an object of class gendis, created by |
... |
other optional arguments |
list of within-sex correlations matrices per population (invisible)
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502ter Braak (2019)
gendis, summary.gendis, predict.gendis.
data("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDFdata("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDF
summary.gendis summarizes the results of gendis.
## S3 method for class 'gendis' summary(object, ...)## S3 method for class 'gendis' summary(object, ...)
object |
an object of class gendis, created by |
... |
other optional arguments. |
GDF
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502ter Braak (2019)
gendis, print.gendis,predict.gendis.
data("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDFdata("fulmarin") names(fulmarin) result <- gendis(population = "population", sex = "sex", measurements = "other_variables", verbose = FALSE , data=fulmarin ) result$GDF summary(result) print(result) # populations may have names: fulmarin$pop <- factor(c("a1","a2","a3","a4","a5","a6")[fulmarin$population]) levels(fulmarin$pop) names(fulmarin) result2 <- gendis(population = "pop", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) # all equal should not give numeric differences. #all.equal(result, result2) result2$GDF - result$GDF
unmix generates a cutpoint below which individuals are predicted to be female
(level 1 of factor(sex)) and above which they are predicted to be
male (level 2 of factor(sex)). The cutpoint is at the point of intersection of two normal densities with unequal
means and variances fitted to argument x. This function is used internally in the predict.gendis function.
unmix(x, verbose = FALSE)unmix(x, verbose = FALSE)
x |
a numeric vector of discriminant scores with optional attribute "classnames", e.g. c("female","male") |
verbose |
logical (default = FALSE) |
unmix is an EM algorithm following example 4.3.2 of Titterington et al. (1985). Alternatively,
library flexmix could have been used.
A list consisting of
cutpoint point of equal density of the normal distributions
p1 estimated probability of class 0 ("female"), informally: fraction of individuals in class 0
p2 estimated probability of class 1 ("female"), informally: fraction of individuals in class 0
m1 estimated mean of the normal distribution of class 0
m2 estimated mean of the normal distribution of class 1
v1 estimated variance of the normal distribution of class 0
v2 estimated variance of the normal distribution of class 1
Titterington, D.M., Smith, A.F.M. & Makov, U.E. (1985). Statistical analysis of finite mixture distributions, Wiley, 1985. pages 86/87, example 4.3.2
van Franeker, J A. ter Braak, C J F. 1993. A generalized discriminant for sexing fulmarine petrels from external measurements. The Auk 110: pp 492-502, https://doi.org/10.2307/4088413 https://edepot.wur.nl/249350
data("fulmarin") result <- gendis(population = "population", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) data("JanMayenBirds") #get the measurements in the generalized discriminant function (GFD) from the new data newdata <- as.matrix(JanMayenBirds[, c("HB","BD2","TL","CL")]) # combine the measurements using the coefficients of the GDF GDFscores <- newdata%*% result$GDF[,2] attr(GDFscores,which = "classnames") <- result$classnames # note the attribute classnames with the names to be used in the printout # for first and second level of the factor sex # Calculate the cutpoint using unmix instead of predict.gendis unmix(GDFscores,verbose = TRUE)data("fulmarin") result <- gendis(population = "population", sex = "sex", measurements = c("HB","BD2","TL","CL"), verbose = FALSE , data=fulmarin ) data("JanMayenBirds") #get the measurements in the generalized discriminant function (GFD) from the new data newdata <- as.matrix(JanMayenBirds[, c("HB","BD2","TL","CL")]) # combine the measurements using the coefficients of the GDF GDFscores <- newdata%*% result$GDF[,2] attr(GDFscores,which = "classnames") <- result$classnames # note the attribute classnames with the names to be used in the printout # for first and second level of the factor sex # Calculate the cutpoint using unmix instead of predict.gendis unmix(GDFscores,verbose = TRUE)