Model specification for DEFM

td_ones(m, covar = "")

td_generic(m, mat, covar = "")

td_formula(m, formula, new_name = "")

td_logit_intercept(m, y_indices = as.integer(c()), covar = "")

rule_not_one_to_zero(m, term_indices)

rule_constrain_support(m, term_index, lb, ub)

# S3 method for class 'DEFM'
e1 + e2

Arguments

m: An object of class DEFM.
covar: String. Name of a covariate to use as an interaction for the effect. If equal to "", then no interaction effect. is used. used to weight the term.
mat: Integer matrix. The matrix specifies the type of motif to capture (see details.)
formula: Character scalar (see details).
new_name: Character scalar. Name to be assigned for the new term. if empty, then it builds a name based on the formula.
y_indices: Integer vector with the coordinates to include in the term.
term_indices: Non-negative vector of indices. Indicates which outcomes this rule will apply.
term_index: Non-negative scalar. Which term this rule will apply.
lb, ub: Numeric scalars. Lower and upper bounds.
e1, e2: e1 An object of class DEFM (e1) and a character (e2).

Value

Invisible 0.

Details

In td_generic, users can specify a particular motif to model. Motifs are represented by cells with values equal to 1, for example, the matrix:

represents a transition y0 -> (y1, y2). If 0 is a motif of interest, then the matrix should include 0 to mark zero values.

The function td_formula, will take the formula and generate the corresponding input for defm::counter_transition(). Formulas can be specified in the following ways:

Intercept effect: {...} No transition, only including the current state.
Transition effect: {...} > {...} Includes current and previous states.

The general notation is [0]y[column id]_[row id]. A preceeding zero means that the value of the cell is considered to be zero. The column id goes between 0 and the number of columns in the array - 1 (so it is indexed from 0,) and the row id goes from 0 to m_order.

Both Intercepts and Transition can interact with covariates. Using either the covar argument or, in the case of formulas, x [Covar name], for example:

Intercept effect: {...} x Hispanic interacts with the Hispanic covar.
Transition effect: {...} > {...} x Hispanic Same.

Intercept effects

Intercept effects only involve a single set of curly brackets. Using the 'greater-than' symbol (i.e., <) is only for transition effects. When specifying intercept effects, users can skip the row_id, e.g., y0_0 is equivalent to y0. If the passed row id is different from the Markov order, i.e., row_id != m_order, then the function returns with an error.

Examples:

"{y0, 0y1}" is equivalent to set a motif with the first element equal to one and the second to zero.

Transition effects

Transition effects can be specified using two sets of curly brackets and an greater-than symbol, i.e., {...} > {...}. The first set of brackets, which we call LHS, can only hold row id that are less than m_order.

The term td_logit_intercept will add what is equivalent to an intercept in a logistic regression. When y_indices is specified, then the function will add one intercept per outcome. These can be weighted by a covariate.

The function rule_not_one_to_zero will avoid the transition one to zero in a Markov process.

The function rule_constrain_support will constrain the support of the model by specifying a lower and upper bound for a given statistic.

The + method is a shortcut for term_formula

Examples

# Loading Valtente's SNS data
data(valentesnsList)

mymodel <- new_defm(
  id    = valentesnsList$id,
  Y     = valentesnsList$Y,
  X     = valentesnsList$X,
  order = 1
)

# Conventional regression intercept
td_logit_intercept(mymodel)

# Interaction effect with Hispanic
td_logit_intercept(mymodel, covar = "Hispanic")

# Transition effect from only y1 to both equal to 1.
td_formula(mymodel, "{y1, 0y2} > {y1, y2}")

# Same but interaction with Female
td_formula(mymodel, "{y1, 0y2} > {y1, y2} x Female")

# Inspecting the model
mymodel
#> Num. of Arrays       : 0
#> Support size         : -
#> Support size range   : -
#> Arrays in powerset   : 0
#> Transform. Fun.      : no
#> Model terms (8)    :
#>  - Logit intercept alcohol
#>  - Logit intercept tobacco
#>  - Logit intercept mj
#>  - Logit intercept alcohol x Hispanic
#>  - Logit intercept tobacco x Hispanic
#>  - Logit intercept mj x Hispanic
#>  - Motif {tobacco+, mj-}⇨{tobacco+, mj+}
#>  - Motif {tobacco+, mj-}⇨{tobacco+, mj+} x Female
#> Model Y variables (3):
#>   0) alcohol
#>   1) tobacco
#>   2) mj

# Initializing and fitting
init_defm(mymodel)
defm_mle(mymodel)
#> 
#> Call:
#> stats4::mle(minuslogl = minuslog, start = start, method = "L-BFGS-B", 
#>     nobs = nrow_defm(object) + ifelse(morder_defm(object) > 0, 
#>         -nobs_defm(object), 0L), lower = lower, upper = upper)
#> 
#> Coefficients:
#>                        Logit intercept alcohol 
#>                                     -1.4021661 
#>                        Logit intercept tobacco 
#>                                     -2.8318789 
#>                             Logit intercept mj 
#>                                     -3.0995487 
#>             Logit intercept alcohol x Hispanic 
#>                                      1.5999458 
#>             Logit intercept tobacco x Hispanic 
#>                                      0.9043077 
#>                  Logit intercept mj x Hispanic 
#>                                      1.7451446 
#>          Motif {tobacco+, mj-}⇨{tobacco+, mj+} 
#>                                      3.6516810 
#> Motif {tobacco+, mj-}⇨{tobacco+, mj+} x Female 
#>                                      0.1025614