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Partial least squares Regression beta regression models

Source: R/plsRbeta.R, R/plsRbetamodel.default.R, R/plsRbetamodel.formula.R
plsRbeta.Rd

This function implements Partial least squares Regression generalized linear models complete or incomplete datasets.

Usage

plsRbeta(object, ...)

plsRbetamodel(object, ...)

# Default S3 method
plsRbetamodel(
  object,
  dataX,
  nt = 2,
  limQ2set = 0.0975,
  dataPredictY = dataX,
  modele = "pls",
  family = NULL,
  typeVC = "none",
  EstimXNA = FALSE,
  scaleX = TRUE,
  scaleY = NULL,
  pvals.expli = FALSE,
  alpha.pvals.expli = 0.05,
  MClassed = FALSE,
  tol_Xi = 10^(-12),
  weights,
  method,
  sparse = FALSE,
  sparseStop = TRUE,
  naive = FALSE,
  link = NULL,
  link.phi = NULL,
  type = "ML",
  verbose = TRUE,
  ...
)

# S3 method for class 'formula'
plsRbetamodel(
  object,
  data = NULL,
  nt = 2,
  limQ2set = 0.0975,
  dataPredictY,
  modele = "pls",
  family = NULL,
  typeVC = "none",
  EstimXNA = FALSE,
  scaleX = TRUE,
  scaleY = NULL,
  pvals.expli = FALSE,
  alpha.pvals.expli = 0.05,
  MClassed = FALSE,
  tol_Xi = 10^(-12),
  weights,
  subset,
  start = NULL,
  etastart,
  mustart,
  offset,
  method = "glm.fit",
  control = list(),
  contrasts = NULL,
  sparse = FALSE,
  sparseStop = TRUE,
  naive = FALSE,
  link = NULL,
  link.phi = NULL,
  type = "ML",
  verbose = TRUE,
  ...
)

Arguments

object

a response (training) dataset or an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.

...

arguments to pass to plsRmodel.default or to plsRmodel.formula

dataX

predictor(s) (training) dataset

nt

number of components to be extracted

limQ2set

limit value for the Q2

dataPredictY

predictor(s) (testing) dataset

modele

name of the PLS glm or PLS beta model to be fitted ("pls", "pls-glm-Gamma", "pls-glm-gaussian", "pls-glm-inverse.gaussian", "pls-glm-logistic", "pls-glm-poisson", "pls-glm-polr", "pls-beta"). Use "modele=pls-glm-family" to enable the family option.

family

a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family for details of family functions.) To use the family option, please set modele="pls-glm-family". User defined families can also be defined. See details.

typeVC

type of leave one out cross validation. For back compatibility purpose.

list("none")

no cross validation

list("standard")

no cross validation

list("missingdata")

no cross validation

list("adaptative")

no cross validation

EstimXNA

only for modele="pls". Set whether the missing X values have to be estimated.

scaleX

scale the predictor(s) : must be set to TRUE for modele="pls" and should be for glms pls.

scaleY

scale the response : Yes/No. Ignored since non always possible for glm responses.

pvals.expli

should individual p-values be reported to tune model selection ?

alpha.pvals.expli

level of significance for predictors when pvals.expli=TRUE

MClassed

number of missclassified cases, should only be used for binary responses

tol_Xi

minimal value for Norm2(Xi) and \(\mathrm{det}(pp' \times pp)\) if there is any missing value in the dataX. It defaults to \(10^{-12}\)

weights

an optional vector of 'prior weights' to be used in the fitting process. Should be NULL or a numeric vector.

method

the method to be used in fitting the model. The default method "glm.fit" uses iteratively reweighted least squares (IWLS). User-supplied fitting functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as glm.fit.

sparse

should the coefficients of non-significant predictors (<alpha.pvals.expli) be set to 0

sparseStop

should component extraction stop when no significant predictors (<alpha.pvals.expli) are found

naive

Use the naive estimates for the Degrees of Freedom in plsR? Default is FALSE.

character specification of the link function in the mean model (mu). Currently, "logit", "probit", "cloglog", "cauchit", "log", "loglog" are supported. Alternatively, an object of class "link-glm" can be supplied.

character specification of the link function in the precision model (phi). Currently, "identity", "log", "sqrt" are supported. The default is "log" unless formula is of type y~x where the default is "identity" (for backward compatibility). Alternatively, an object of class "link-glm" can be supplied.

type

character specification of the type of estimator. Currently, maximum likelihood ("ML"), ML with bias correction ("BC"), and ML with bias reduction ("BR") are supported.

verbose

should info messages be displayed ?

data

an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which plsRbeta is called.

subset

an optional vector specifying a subset of observations to be used in the fitting process.

start

starting values for the parameters in the linear predictor.

etastart

starting values for the linear predictor.

mustart

starting values for the vector of means.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. One or more offset terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See model.offset.

control

a list of parameters for controlling the fitting process. For glm.fit this is passed to glm.control.

contrasts

an optional list. See the contrasts.arg of model.matrix.default.

formula

The details of model specification are given under 'Details'.

Value

Depends on the model that was used to fit the model.

Details

There are seven different predefined models with predefined link functions available :

list("\"pls\"")

ordinary pls models

list("\"pls-glm-Gamma\"")

glm gaussian with inverse link pls models

list("\"pls-glm-gaussian\"")

glm gaussian with identity link pls models

list("\"pls-glm-inverse-gamma\"")

glm binomial with square inverse link pls models

list("\"pls-glm-logistic\"")

glm binomial with logit link pls models

list("\"pls-glm-poisson\"")

glm poisson with log link pls models

list("\"pls-glm-polr\"")

glm polr with logit link pls models

Using the "family=" option and setting "modele=pls-glm-family" allows changing the family and link function the same way as for the glm function. As a consequence user-specified families can also be used.

The

accepts the links (as names) identity, log and inverse.

list("gaussian")

accepts the links (as names) identity, log and inverse.

family

accepts the links (as names) identity, log and inverse.

The

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

list("binomial")

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

family

accepts the links logit, probit, cauchit, (corresponding to logistic, normal and Cauchy CDFs respectively) log and cloglog (complementary log-log).

The

accepts the links inverse, identity and log.

list("Gamma")

accepts the links inverse, identity and log.

family

accepts the links inverse, identity and log.

The

accepts the links log, identity, and sqrt.

list("poisson")

accepts the links log, identity, and sqrt.

family

accepts the links log, identity, and sqrt.

The

accepts the links 1/mu^2, inverse, identity and log.

list("inverse.gaussian")

accepts the links 1/mu^2, inverse, identity and log.

family

accepts the links 1/mu^2, inverse, identity and log.

The

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

list("quasi")

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

family

accepts the links logit, probit, cloglog, identity, inverse, log, 1/mu^2 and sqrt.

The function

can be used to create a power link function.

list("power")

can be used to create a power link function.

A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. A terms specification of the form first + second indicates all the terms in first together with all the terms in second with any duplicates removed.

A specification of the form first:second indicates the the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first + second + first:second.

The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on: to avoid this pass a terms object as the formula.

Non-NULL weights can be used to indicate that different observations have different dispersions (with the values in weights being inversely proportional to the dispersions); or equivalently, when the elements of weights are positive integers w_i, that each response y_i is the mean of w_i unit-weight observations.

The default estimator for Degrees of Freedom is the Kramer and Sugiyama's one which only works for classical plsR models. For these models, Information criteria are computed accordingly to these estimations. Naive Degrees of Freedom and Information Criteria are also provided for comparison purposes. For more details, see Kraemer, N., Sugiyama M. (2010). "The Degrees of Freedom of Partial Least Squares Regression". preprint, http://arxiv.org/abs/1002.4112.

Note

Use plsRbeta instead.

References

Frédéric Bertrand, Nicolas Meyer, Michèle Beau-Faller, Karim El Bayed, Izzie-Jacques Namer, Myriam Maumy-Bertrand (2013). Régression Bêta PLS. Journal de la Société Française de Statistique, 154(3):143-159. https://ojs-test.apps.ocp.math.cnrs.fr/index.php/J-SFdS/article/view/215

See also

plsR and plsRglm

Author

Frédéric Bertrand
frederic.bertrand@lecnam.net
https://fbertran.github.io/homepage/

Examples



data("GasolineYield",package="betareg")
modpls <- plsRbeta(yield~.,data=GasolineYield,nt=3,modele="pls-beta")
#> ____************************************************____
#> 
#> Model: pls-beta 
#> 
#> Link: logit 
#> 
#> Link.phi: 
#> 
#> Type: ML 
#> 
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X or Y____
#> ****________________________________________________****
#> 
modpls$pp
#>              Comp_ 1     Comp_ 2     Comp_ 3
#> gravity   0.37895923 -0.42864981  0.50983922
#> pressure  0.61533000 -0.41618828 -0.01737302
#> temp10   -0.50627633  0.47379983 -0.47750566
#> temp      0.30248369  0.60751756  0.28239621
#> batch1    0.50274128 -0.30221156 -0.25801764
#> batch2   -0.14241033 -0.13859422  0.80068659
#> batch3   -0.04388172 -0.17303214  0.48564161
#> batch4    0.11299471 -0.08302689  0.04755182
#> batch5    0.23341035  0.08396326 -0.51238456
#> batch6    0.07974302  0.07209943 -0.30710455
#> batch7   -0.37365392 -0.02133356  0.81852001
#> batch8   -0.12891598  0.16967195 -0.06904725
#> batch9   -0.02230288  0.19425476 -0.57189134
#> batch10  -0.25409429  0.28587553 -0.61277072
modpls$Coeffs
#>                    [,1]
#> Intercept -4.1210566075
#> gravity    0.0157208676
#> pressure   0.0305159627
#> temp10    -0.0074167766
#> temp       0.0108057945
#> batch1     0.0910284844
#> batch2     0.1398537354
#> batch3     0.2287070464
#> batch4    -0.0008124326
#> batch5     0.1018679027
#> batch6     0.1147971957
#> batch7    -0.1005469609
#> batch8    -0.0447907428
#> batch9    -0.0706292318
#> batch10   -0.1984703429
modpls$Std.Coeffs
#>                    [,1]
#> Intercept -1.5526788976
#> gravity    0.0885938394
#> pressure   0.0799466277
#> temp10    -0.2784359925
#> temp       0.7537685874
#> batch1     0.0305865495
#> batch2     0.0414169259
#> batch3     0.0677303525
#> batch4    -0.0002729861
#> batch5     0.0301676274
#> batch6     0.0339965674
#> batch7    -0.0337848600
#> batch8    -0.0132645358
#> batch9    -0.0173701781
#> batch10   -0.0587759166
modpls$InfCrit
#>                  AIC        BIC Chi2_Pearson_Y      RSS_Y pseudo_R2_Y      R2_Y
#> Nb_Comp_0  -52.77074  -49.83927       30.72004 0.35640772          NA        NA
#> Nb_Comp_1  -87.96104  -83.56383       31.31448 0.11172576   0.6879757 0.6865226
#> Nb_Comp_2 -114.10269 -108.23975       33.06807 0.04650238   0.8671800 0.8695248
#> Nb_Comp_3 -152.71170 -145.38302       30.69727 0.01138837   0.9526757 0.9680468
modpls$PredictY[1,]
#>    gravity   pressure     temp10       temp     batch1     batch2     batch3 
#>  2.0495333  1.6866554 -1.3718198 -1.8219769  2.6040833 -0.3165683 -0.3165683 
#>     batch4     batch5     batch6     batch7     batch8     batch9    batch10 
#> -0.3720119 -0.3165683 -0.3165683 -0.3720119 -0.3165683 -0.2541325 -0.3165683 
rm("modpls")

data("GasolineYield",package="betareg")
yGasolineYield <- GasolineYield$yield
XGasolineYield <- GasolineYield[,2:5]
modpls <- plsRbeta(yGasolineYield,XGasolineYield,nt=3,modele="pls-beta")
#> ____************************************************____
#> 
#> Model: pls-beta 
#> 
#> Link: logit 
#> 
#> Link.phi: 
#> 
#> Type: ML 
#> 
#> ____Component____ 1 ____
#> ____Component____ 2 ____
#> ____Component____ 3 ____
#> ____Predicting X without NA neither in X nor in Y____
#> ****________________________________________________****
#> 
modpls$pp
#>             Comp_ 1    Comp_ 2    Comp_ 3
#> gravity   0.4590380 -0.4538663 -2.5188256
#> pressure  0.6395524 -0.4733525  0.6488823
#> temp10   -0.5435643  0.5292108 -1.3295905
#> temp      0.5682795  0.5473174 -0.2156423
modpls$Coeffs
#>                   [,1]
#> Intercept -3.324462308
#> gravity    0.001577508
#> pressure   0.072027686
#> temp10    -0.008398771
#> temp       0.010365973
modpls$Std.Coeffs
#>                   [,1]
#> Intercept -1.547207763
#> gravity    0.008889933
#> pressure   0.188700277
#> temp10    -0.315301401
#> temp       0.723088389
modpls$InfCrit
#>                  AIC        BIC Chi2_Pearson_Y      RSS_Y pseudo_R2_Y      R2_Y
#> Nb_Comp_0  -52.77074  -49.83927       30.72004 0.35640772          NA        NA
#> Nb_Comp_1 -112.87383 -108.47662       30.57369 0.05211039   0.8498691 0.8537900
#> Nb_Comp_2 -136.43184 -130.56889       30.97370 0.02290022   0.9256771 0.9357471
#> Nb_Comp_3 -139.08440 -131.75572       31.08225 0.02022386   0.9385887 0.9432564
modpls$PredictY[1,]
#>   gravity  pressure    temp10      temp 
#>  2.049533  1.686655 -1.371820 -1.821977 
rm("modpls")