Three-Mode Principal Components: Tuckers Models

Description

This package performs Three-Mode Principal Components using Tuckers Models and plot interactive Biplot. These Three-Mode Principal Component Analysis, provides both useful analytic and graphic tools to study and characterize phytogenetic resources, specially when the influence of environmental factors are possible.

Author(s)

Marta Marticorena, Gustavo Gimenez, Cecilia Gonzalez, Sergio Bramardi

Aplication of the Diffit method.

Description

The diffit method is used to apply when we need to know the axis number to be gathered in the P mode, and Q mode. The third mode, K it is related to the environment numbers. The diffit method consist on fitting each value with the Tuckle algorithm.

Usage

diffit(datos, amb = 2, stand = TRUE, niter = 10000)

Arguments

Details

The final result is the model which has the most coefficient diffits the greatest variability explained and the one which exceed the threshold.

Value

saldiffit a list with a combination numbers of axis, percentage of variability explained and Diffit rate. The critic value or threhold is also return.

Author(s)

Marta Marticorena, Gustavo Gimenez, Cecilia Gonzalez, Sergio Bramardi

References

MARTICORENA, M.; BRAMARDI, S.; DEFACIO, R. 2010.

Characterization of maize populations in different environmental conditions by means of Three-Mode Principal Components Analysis. Revista Ciencia e Investigacion Agraria. 37(3): 93-105.

Timmerman, M.E., and H. Kiers. 2000.

Three-mode principal components analysis. Choosing numbers of components and sensitivity to local optima. The British Journal of the Mahematical and Statistical Psychology 53: 1-16.

Examples

#Copy and paste this example in your console without the comment
#data(maize_pop,package = "tuckerR.mmgg")
#dif_sal <- diffit(maize_pop,amb=2)
#print(dif_sal) the best combination is 3 3 2

31 Native Populations of Maize from Province of Buenos Aires

Description

These populations are part of collection of local populations corresponding to different races that are conserved in the Active Germplasm Bank of INTA Pergamino Experimental Station, Argentina.

Usage

data("maize_pop")

Format

A data frame with 10 characteristics of 31 maize populations in two different conditions corresponding to production areas of Buenos Aires. Since the variables are repeated in both places the data frame has a total of 20 variables, 10 for an environment and evaluated them in the other conditions. First and second conditions the numerical vectors are the following:

LMZ

a numeric vector with ear length(cm), in first condition

DMZ

a numeric vector with ear diameter (mm),in first condition

AGR

a numeric vector with grain width (mm),in first condition

LGR

a numeric vector with grain length (cm), in first condition

PROL

a numeric vector prolicicacy (ears/plant), in first condition

GRXM

a numeric vector with grains by meter in first condition

PESO_1000

a numeric vector with weight of 1000 grains (grs)

REND

a numeric vector with yield (kg/ha), in first condition

ALTPL

a numeric vector height of the plant (cm) in first condition

ALTMZ

a numeric vector with height of ear insertion (cm) in first condition

LMZ

a numeric vector with ear length(cm), in second condition

DMZ

a numeric vector with ear diameter (mm),in second condition

AGR

a numeric vector with grain width (mm),in second condition

LGR

a numeric vector with grain length (cm), in second condition

PROL

a numeric vector prolicicacy (ears/plant), in second condition

GRXM

a numeric vector with grains by meter in second condition

PESO_1000

a numeric vector with weight of 1000 grains (grs) in second condition

REND

a numeric vector with yield (kg/ha), in second condition

ALTPL

a numeric vector height of the plant (cm) in second condition

ALTMZ

a numeric vector with height of ear insertion (cm) in second condition

Details

Ten quantitative variables were evaluated in two tests conducted in the 2003/04 season in the localities Pergamino A INTA) and Ferre. These variables allowed for morphologic-agronomic characterization and may be influenced, to a certain extent, by environmental conditions.

References

MARTICORENA, M.; BRAMARDI, S.; DEFACIO, R. (2010). Characterization of maize populations in different environmental conditions by means of Three-Mode Principal Components Analysis. Revista Ciencia e Investigacion Agraria. 37(3): 93-105.

Examples

data(maize_pop,package = "tuckerR.mmgg")
str(maize_pop); summary(maize_pop)

Concatenate data frame in array and matrix by cases, variables and environments

Description

Concatenate data frame in array and matrix by cases, variables and environments to performs three mode principal components with the function tucker2R.

Usage

matrition(datos, I, J, K)

Arguments

Details

This process is also knowing as 'matricizing' or 'unfolding'.

Value

matrizlista return a list with: the array "m" with all the data concatenate in array. X1 the data is concatenate by cases, X2 the data concatenate by variables and X3 the data concatenate by environments.

Examples

data(maize_pop,package = "tuckerR.mmgg")
conc_matrix <- matrition(maize_pop,I=30,J=10,K=2)
conc_matrix$m  #get m array
conc_matrix$X1 #get matrix by cases
conc_matrix$X2 #get matrix by variables
conc_matrix$X3 #get matrix by environments

Plot an interactive Biplot

Description

The interactive Biplot consists of combining two of the modes, obtaining markers for the individuals and vectors for the variables that were concatenated with the conditions. To plot the interactive Biplot this function need the output for the tucker2R function.

Usage

plot(saltuck, ...)

## S3 method for class 'marta'
plot(saltuck)

Arguments

Details

The interactive Biplot allows for the visualization of the inter structure of the differents data tables.

Value

NULL

Author(s)

Marta Marticorena, Gustavo Gimenez, Cecilia Gonzalez, Sergio Bramardi

References

MARTICORENA, M.; BRAMARDI, S.; DEFACIO, R. 2010.

Characterization of maize populations in different environmental conditions by means of Three Mode Principal Components Analysis. Revista Ciencia e Investigacion Agraria. 37(3): 93-105.

Gabriel, K.R. 1971.

The biplot graphic display of matrices with appications to principal components analysis. Biometrika. 58, 453-467.

Examples

data(maize_pop,package = "tuckerR.mmgg")
prueba1 <- tucker2R(maize_pop, amb=2, stand=TRUE, nc1=3, nc2=3)
plot(prueba1)

Three-Mode Principal Components: Tucker 2 Model

Description

This function performs Three-Mode Principal Components using Tucker-2 Model.Compute all the output necessary to plot interactive Biplot.The Three-Mode Principal Component Analysis, provides both useful analytic and graphic tools to study and characterize phytogenetic resources, especially when the influence of environmental factors are possible.

Usage

tucker2R(datos, amb= 2, stand = TRUE, nc1 = 2, nc2 = 2, niter = 10000)

Arguments

Details

To determine the number of components that are going to be retained, we use previously to the algorithm applications,method called DifFit. The number of components in the third mode is obtained from the number of conditions.The labels of the variables must be the same for all conditions in the data frame.

Value

Resultado a list which stores the name of the individual and the variables, the number of iterations, the variability explained by the model, and the total variability. Proyeccion It is a list which holds the projection of individuals and variables to see if the biplot is difficult to understand because of the huge number of cases or plotted vectors. saltuck is a list with the results of the algorithm to plot the biplot, where the names of the conditions are well kept.

Author(s)

Marta Marticorena, Gustavo Gimenez, Cecilia Gonzalez, Sergio Bramardi

References

Marticorena, M.; Bramardi, S.; Defacio, R. 2010.

Characterization of maize populations in different environmental conditions by means of Three-Mode Principal Components Analysis. Revista Ciencia e Investigacion Agraria. 37(3): 93-105.

Timmerman, M.E., and H. Kiers. 2000.

Three-mode principal components analysis. Choosing numbers of components and sensitivity to local optima. The British Journal of the Mahematical and Statistical Psychology 53: 1-16.

See Also

The function plot.marta for a complete analisis.

Examples

data(maize_pop,package = "tuckerR.mmgg")
(output <- tucker2R(maize_pop,amb=2,stand=TRUE,nc1=3,nc2=3))