M-step driver to be used in flexmix

Description

Function used in flexmix M-Step to estimate hybrid model

Usage

FLXMRhyreg(
  formula = . ~ .,
  family = c("hyreg"),
  type = NULL,
  type_cont = NULL,
  type_dich = NULL,
  variables_both = NULL,
  variables_cont = NULL,
  variables_dich = NULL,
  stv = NULL,
  offset = NULL,
  opt_method = "BFGS",
  optimizer = "optim",
  lower = -Inf,
  upper = Inf,
  ...
)

Arguments

Value

a model object, that can be used in hyreg2 as input for parameter model in flexmix::flexmix()

a model object, that can be used in hyreg2 as input for parameter model in flexmix::flexmix

Author(s)

Svenja Elkenkamp and Kim Rand

Examples

formula <- y ~  -1 + x1 + x2 + x3
the$k <- 2
stv <- setNames(c(0.2,0,1,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))



x <- model.matrix(formula,simulated_data_norm)
y <- simulated_data_norm$y
w <- 1
model <- FLXMRhyreg(formula = formula,
                    family=c("hyreg"),
                    type =  simulated_data_norm$type,
                    stv = stv,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = list(iter.max = 1000, verbose = 4),
                    offset = NULL,
                    optimizer = "optim",
                    variables_both =  names(stv)[!is.element(names(stv),c("sigma","theta"))],
                    variables_cont = NULL,
                    variables_dich = NULL,
                    lower = -Inf,
                    upper = Inf,
)

M-step driver to be used in flexmix accounting for heteroscedastisity

Description

Function used in flexmix M-Step to estimate hybrid model accounting for heteroscedastisity

Usage

FLXMRhyreg_het(
  data,
  formula = . ~ .,
  formula_sigma = formula_sigma,
  family = c("hyreg"),
  type = NULL,
  type_cont = NULL,
  type_dich = NULL,
  variables_both = NULL,
  variables_cont = NULL,
  variables_dich = NULL,
  stv = NULL,
  stv_sigma = NULL,
  offset = NULL,
  opt_method = "BFGS",
  optimizer = "optim",
  lower = -Inf,
  upper = Inf,
  ...
)

Arguments

Value

a model object, that can be used in hyreg2_het as input for parameter model in flexmix::flexmix()

Author(s)

Svenja Elkenkamp and Kim Rand

Examples

formula <- y ~  -1 + x1 + x2 + x3
formula_sigma <- y ~ x1 + x2 + x3
stv <- setNames(c(0.2,0,1,1),c(colnames(simulated_data_norm)[3:5],c("theta")))
stv_sigma <- setNames(c(0.2,0.2,0.1,1),c(colnames(simulated_data_norm)[3:5],c("(Intercept)")))


x <- model.matrix(formula,simulated_data_norm)
y <- simulated_data_norm$y
w <- 1
model <- FLXMRhyreg_het( data = simulated_data_norm,
                     formula = formula,
                     formula_sigma = formula_sigma,
                    family=c("hyreg"),
                    type =  simulated_data_norm$type,
                    stv = stv,
                    stv_sigma = stv_sigma,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = list(iter.max = 1000, verbose = 4),
                    offset = NULL,
                    optimizer = "optim",
                    variables_both =  names(stv)[!is.element(names(stv),c("theta"))],
                    variables_cont = NULL,
                    variables_dich = NULL,
                    lower = -Inf,
                    upper = Inf,
)

extract parameter estimates as named vector

Description

function to export coefficient values and names from a model fitted with hyreg2 or hyreg2_het These values can be used as stv for a new model with k > 1

Usage

get_stv(mod, comp = "Comp.1")

Arguments

Value

⁠named vector⁠ of parameter estimates from mod. Can be used as stv for additional model estimations using hyreg2 or hyreg2_het

Author(s)

Svenja Elkenkamp

Examples

formula <- y ~  -1 + x1 + x2 + x3 | id

k <- 1
stv <- setNames(c(0.2,0,1,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))
control = list(iter.max = 1000, verbose = 4)
rm(counter)
mod <- hyreg2(formula = formula,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type,
                    stv = stv,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "both",
                    id_col = "id"
)
new_stv <- get_stv(mod)

# these new_stv can be used in an other estimation using hyreg2 as stv

function to decode which group or observation was classified to which class by the model

Description

This function can be used to decode the classified classes by the model generates using hyreg2 or hyreg2_het and see, which group or observation was signed to which class

Usage

give_id(data, model, id_col = NULL)

Arguments

Value

dataframe of two columns, first column named as provided id_col or "observation" if id_col was not given as an input. second column named "mod_comp" indicating the assigned class for this group or observation

Author(s)

Svenja Elkenkamp & John Grosser

Examples

# estimate a model using simulated_data_rnorm

### using grouping variable id ####
formula <- y ~  -1 + x1 + x2 + x3 | id
k <- 1
stv <- setNames(c(0.2,0.2,0.2,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))
control <- list(iter.max = 1000, verbose = 4)

hyflex_mod <- hyreg2(formula = formula,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type,
                    stv = stv,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "both",
                    id_col = "id"
)
# use of function give_id
give_id(data = simulated_data_norm,
model = hyflex_mod,
id_col = "id")

function for model estimation for EQ-5D valuesets

Description

Estimation of hybrid model for EQ-5D data

Usage

hyreg2(
  formula,
  data,
  type,
  type_cont,
  type_dich,
  k = 1,
  control = NULL,
  stv = NULL,
  offset = NULL,
  opt_method = "BFGS",
  optimizer = "optim",
  lower = -Inf,
  upper = Inf,
  latent = "both",
  id_col = NULL,
  classes_only = FALSE,
  variables_both = NULL,
  variables_dich = NULL,
  variables_cont = NULL,
  ...
)

Arguments

Details

see details of different inputs listed below

Value

model object of type flexmix or list of model objects of type flexmix

formula

a typical R formula of the form ⁠y ~ x1 + x2 + …⁠ should be provided. Additionally, it is possible to include a grouping variable for repeated measures by using ⁠“| xg”⁠ where xg is the column containing the group-memberships. The resulting formula will look like this: ⁠y ~ x1 + x2 +… | xg⁠. In flexmix, this is called the concomitant variable specification: the model is fit conditional on grouping, so that all observations with the same group are treated as belonging together when computing likelihood contributions. One possible grouping variable can be an id number to identify answers by the same participants. We highly recommend using a grouping variable, since otherwise the algorithm for k = 2 tends to classify all continuous data into one estimated class and all dichotomous data into the other.

data

a dataframe having the following columns: all independent variables (x) and the dependent variable y used in formula, one column for the grouping variable xg if grouping should be used, e.g. id numbers of participants with repeated measurements, one column indicating if the observations belongs to continuous or dichotomous data with the entries type_cont and type_dich (e.g., for a column called "type" with the entries "TTO" for continuous datapoints and "DCE" for dichotomous datapoints, type_cont will be "TTO" and type_dich will be "DCE"). One row should match one observation (one datapoint).

start values (stv)

if the same start values stv are to be used for all latent classes, the given start values must be a ⁠named vector⁠. Otherwise (if different start values are assumed for each latent class), a list of named vectors should be used . In this case, there must be one entry in the list for each latent class. Each start value vector must include start values for sigma and theta. Currently, it is necessary to use the names "sigma" and "theta" for these values. If users are unsure for which variables start values must be provided, this can be checked by calling colnames(model.matrix(formula,data)). In this call, the formula should not include the grouping variable.

latent, id_col, classes_only

in some situations, it can be useful to identify the latent classes on only one type of data while estimating the model parameters on both types of data. In such cases, the input variable latent can be used to specify on which type of data the classification should be done. If ⁠“cont”⁠ or ⁠“dich”⁠ is used, the input parameter id_col must be specified and gives the name, i.e. a ⁠character string⁠, of the grouping variable for classification. Some groups may be removed from the data, since they have only continuous or only dichotomous observations. Then in a first step, a model is estimated only on the continuous/dichotomous data and the achieved classification is stored. In a next step, model parameters are estimated separately for each identified class on both types of data using this classification. The output object of hyreg2 in this case is a list of k models. Additionally, at position k+1 of the list, a data frame containing the corresponding classifications from the first step is returned. Each element k in the list contains the estimated parameters for one of the latent classes. When setting the input variable classes_only to TRUE, the second step is left out and the estimated classes from step one are given as output.

variables_both, variables_cont, variables_dich

It is possible to specify partial coefficients, which are used only on continuous or dichotomous data.

• Example: Suppose different models should be specified for continuous and dichotomous data:

• Model continuous data: y ~ x1 + x3

• Model dichotomous data: y ~ x1 + x2

• The formula input to hyreg2 must then include all parameters that occur in either model: y ~ x1 + x2 + x3

• The assignment of parameters to data types is then achieved via the input arguments variables_both, variables_cont, and variables_dich:

• variables_both = ⁠“x1”⁠,

• variables_cont = ⁠“x3”⁠ and

• variables_dich = ⁠“x2”⁠.

• Every variable included in the provided formula (except the grouping variable ) must appear in exactly one of these vectors. One of the variables_ vectors can also be NULL, if no variables should be used only on this type of the data.

Author(s)

Svenja Elkenkamp, Kim Rand and John Grosser

Examples

formula <- y ~  -1 + x1 + x2 + x3 | id

k <- 2
stv <- setNames(c(0.2,0,1,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))
control = list(iter.max = 1000, verbose = 4)
rm(counter)
mod <- hyreg2(formula = formula,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type, # also "type" would work
                    stv = stv,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "cont",
                    id_col = "id"
)
summary_hyreg2(mod)

function for model estimation for EQ-5D valueset data accounting for heteroscedasticity in continous data

Description

Estimation of hybrid model for EQ-5D data

Usage

hyreg2_het(
  formula,
  formula_sigma = NULL,
  data,
  type,
  type_cont,
  type_dich,
  k = 1,
  control = NULL,
  stv = NULL,
  stv_sigma = NULL,
  offset = NULL,
  opt_method = "BFGS",
  optimizer = "optim",
  lower = -Inf,
  upper = Inf,
  latent = "both",
  id_col = NULL,
  classes_only = FALSE,
  variables_both = NULL,
  variables_dich = NULL,
  variables_cont = NULL,
  ...
)

Arguments

Details

see details of different inputs listed below

Value

model object of type flemix, coefficients named ..._h are coefficients for heteroscedasticity

formula

a typical R formula of the form ⁠y ~ x1 + x2 + …⁠ should be provided. Additionally, it is possible to include a grouping variable for repeated measures by using ⁠“| xg”⁠ where xg is the column containing the group-memberships. The resulting formula will look like this: ⁠y ~ x1 + x2 +… | xg⁠. In flexmix, this is called the concomitant variable specification: the model is fit conditional on grouping, so that all observations with the same group are treated as belonging together when computing likelihood contributions. One possible grouping variable can be an id number to identify answers by the same participants. We highly recommend using a grouping variable, since otherwise the algorithm for k = 2 tends to classify all continuous data into one estimated class and all dichotomous data into the other.

data

a dataframe having the following columns: all independent variables (x) and the dependent variable y used in formula, one column for the grouping variable xg if grouping should be used, e.g. id numbers of participants with repeated measurements, one column indicating if the observations belongs to continuous or dichotomous data with the entries type_cont and type_dich (e.g., for a column called "type" with the entries "TTO" for continuous datapoints and "DCE" for dichotomous datapoints, type_cont will be "TTO" and type_dich will be "DCE"). One row should match one observation (one datapoint).

start values (stv)

if the same start values stv are to be used for all latent classes, the given start values must be a ⁠named vector⁠. Otherwise (if different start values are assumed for each latent class), a list of named vectors should be used . In this case, there must be one entry in the list for each latent class. Each start value vector must include start values for sigma and theta. Currently, it is necessary to use the names "sigma" and "theta" for these values. If users are unsure for which variables start values must be provided, this can be checked by calling colnames(model.matrix(formula,data)). In this call, the formula should not include the grouping variable.

formula_sigma, stv_sigma

To account for heteroscedasticity in the data, an additional formula formula_sigma and an additional vector of starting values for this formula (stv_sigma) can be specified. The provided formula_sigma must be linear and the vector stv_sigma must contain start values for all parameters used in the formula. If neither formula_sigma nor stv_sigma are provided, the same inputs as for formula (without controlling for groups) and stv (without sigma) are used. The estimates for sigma can be identified in the model output by the ending "_h". It is important to note that, when using hyreg2_het, neither stv nor stv_sigma are allowed to include sigma, because sigma is estimated with its own formula (in contrast to hyreg2, where sigma must always be specified in stv).

latent, id_col, classes_only

in some situations, it can be useful to identify the latent classes on only one type of data while estimating the model parameters on both types of data. In such cases, the input variable latent can be used to specify on which type of data the classification should be done. If ⁠“cont”⁠ or ⁠“dich”⁠ is used, the input parameter id_col must be specified and gives the name, i.e. a ⁠character string⁠, of the grouping variable for classification. Some groups may be removed from the data, since they have only continuous or only dichotomous observations. Then in a first step, a model is estimated only on the continuous/dichotomous data and the achieved classification is stored. In a next step, model parameters are estimated separately for each identified class on both types of data using this classification. The output object of hyreg2 in this case is a list of k models. Additionally, at position k+1 of the list, a data frame containing the corresponding classifications from the first step is returned. Each element k in the list contains the estimated parameters for one of the latent classes. When setting the input variable classes_only to TRUE, the second step is left out and the estimated classes from step one are given as output.

variables_both, variables_cont, variables_dich

It is possible to specify partial coefficients, which are used only on continuous or dichotomous data.

• Example: Suppose different models should be specified for continuous and dichotomous data:

• Model continuous data: y ~ x1 + x3

• Model dichotomous data: y ~ x1 + x2

• The formula input to hyreg2 must then include all parameters that occur in either model: y ~ x1 + x2 + x3

• The assignment of parameters to data types is then achieved via the input arguments variables_both, variables_cont, and variables_dich:

• variables_both = ⁠“x1”⁠,

• variables_cont = ⁠“x3”⁠ and

• variables_dich = ⁠“x2”⁠.

• Every variable included in the provided formula (except the grouping variable ) must appear in exactly one of these vectors. One of the variables_ vectors can also be NULL, if no variables should be used only on this type of the data.

Author(s)

Svenja Elkenkamp, Kim Rand and John Grosser

Examples

formula <- y ~  -1 + x1 + x2 + x3
formula_sigma <- y ~  x1 + x2 + x3

k <- 1
stv <- setNames(c(0.2,0,1,1),c(colnames(simulated_data_norm)[3:5],c("theta")))
stv_sigma <- setNames(c(0.2,0,1,1),c(colnames(simulated_data_norm)[3:5],c("(Intercept)")))
control = list(iter.max = 1000, verbose = 4)
rm(counter)
mod <- hyreg2_het(formula = formula,
                   formula_sigma = formula_sigma,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type, # or "type"
                    stv = stv,
                    stv_sigma = stv_sigma,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "both",
                    id_col = "id"
)
summary_hyreg2(mod)

plot function to visualize the classification based on the model estimated using hyreg2 or hyreg2_het

Description

This function can be used to visualize the classification based on the model for different variables. ggplot2::ggplot() is used.

Usage

plot_hyreg2(
  data,
  x,
  y,
  id_col,
  id_df_model,
  type_to_plot = NULL,
  colors = NULL
)

Arguments

Details

id_col_df has to be provided anyway, even if the model was estimated without grouping variable. Since there might be no grouping varibale in the data, we recommend to create a new column called "observation" in data using the rownames/observationnumbers as charachter values and use this column as input for id_col in plot_hyreg2, additionally you can then use id_df_model = give_id(data,model,"observation"), see example

Value

ggplot object visualizing x against y by classes from the model

Author(s)

Svenja Elkenkamp & John Grosser

Examples

# estimate a model using simulated_data_rnorm

formula <- y ~  -1 + x1 + x2 + x3 | id
k <- 2
stv <- setNames(c(0.2,0.2,0.2,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))
control <- list(iter.max = 1000, verbose = 4)

hyflex_mod <- hyreg2(formula = formula,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type,
                    stv = stv,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "cont",
                    id_col = "id"
)
# plotting the variables id against y
plot_hyreg2(data = simulated_data_norm,
          x = "id",
          y = "y",
          id_col = "id",
          id_df_model = give_id(data = simulated_data_norm,
                                model = hyflex_mod,
                                id = "id"))

simulated_data

Description

simulated_data

Usage

simulated_data

Format

simulated_data

A simulated data frame with 480 rows and 25 columns, following a combination of normal and binomial distribution

type

type of data

y

result of the model y = -1 + mo2 + mo3 + ... + ad4 + ad5

mo2, mo3, mo4, mo5, sc2, sc3, sc4, sc5, ua2, ua3, ua4, ua5, pd2, pd3, pd4, pd5,, ad2, ad3, ad4, ad5,

dummy variables for EQ5D data simulation

class

original class of the data point

id

id number of observations to simulated different persons

y_cens

column y censored at 2 (upper boundary)

...

Source

simulated with true parameter values: Class 1: sigma = XXX, theta = XXX and c(mo2,mo3,mo4,mo5, XXX) = c(XXX) Class 2: sigma = XXX, theta = XXX and c(mo2,mo3,mo4,mo5, XXX) = c(XXX)

simulated_data_mo

Description

simulated_data_mo

Usage

simulated_data_mo

Format

simulated_data_mo

A simulated data frame with 480 rows and 9 columns, following a combination of normal and binomial distribution

type

type of data

y

result of the model y = -1 + mo2 + mo3 + mo4 + mo5

mo2, mo3, mo4, mo5

dummy variables

class

original class of the data point

id

id number of observations to simulated different persons

y_cens

column y censored at 0 (lower boundary)

...

Source

simulated with true parameter values: Class 1: sigma = XXX, theta = XXX and c(mo2,mo3,mo4,mo5) = c(XXX) Class 2: sigma = XXX, theta = XXX and c(mo2,mo3,mo4,mo5) = c(XXX)

simulated_data_norm

Description

simulated_data_norm

Usage

simulated_data_norm

Format

simulated_data_norm

A simulated data frame with 600 rows and 8 columns, following a combination of normal and binomial distribution

type

type of data

y

result of the model y = x1 + x2 + x3

x1, x2, x3

random numbers from rnorm

class

original class of the data point

id

id number of observations to simulated different persons

y_cens

column y censored at 3

...

Source

simulated with true parameter values: Class 1: sigma = 1.0, theta = 5 and c(x1,x2,x3) = c(0.5, -0.3, 0.8) Class 2: sigma = 0.5, theta = 2 and c(x1,x2,x3) = c(1.4, 2.3, -0.2)

construct model summary as in base R

Description

get model parameters of model generated by hyreg2 oder hyreg2_het

Usage

summary_hyreg2(object)

Arguments

Value

summary object of bbmle::mle2() model

Author(s)

Svenja Elkenkamp

Examples

formula <- y ~  -1 + x1 + x2 + x3 | id
k <- 1
stv <- setNames(c(0.2,0,1,1,1),c(colnames(simulated_data_norm)[3:5],c("sigma","theta")))
control = list(iter.max = 1000, verbose = 4)
rm(counter)
mod <- hyreg2(formula = formula,
                    data =  simulated_data_norm,
                    type =  simulated_data_norm$type,
                    stv = stv,
                    k = k,
                    type_cont = "TTO",
                    type_dich = "DCE_A",
                    opt_method = "L-BFGS-B",
                    control = control,
                    latent = "both",
                    id_col = "id"
)
summary_hyreg2(mod)

creating environment for package internal objects

Description

creating environment for package internal objects

Usage

the

Format

An object of class environment of length 1.