Model specification for DEFM

term_defm_ones(m, idx = "", vname = "")

term_defm_fe(m, idx = "", k = 1, vname = "")

term_defm_transition(m, mat, idx = "", vname = "")

term_defm_transition_formula(m, formula, idx = "", vname = "")

term_defm_logit_intercept(m, coords = as.integer(c()), idx = "", vname = "")

rule_not_one_to_zero(m, idx)

rule_constrain_support(m, idx, lb, ub)

# S3 method for DEFM
+(e1, e2)

Arguments

m: An object of class DEFM.
idx: Character scalar. Name of the variable to include in the term.
vname: Character scalar. Name to be assigned for the new term.
k: Numeric scalar. Exponent used in the term.
mat: Integer matrix. The matrix specifies the type of motif to capture (see details.)
formula: Character scalar (see details).
coords: Integer vector with the coordinates to include in the term.
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 term_defm_transition, 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 term_defm_transition_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.

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 term_defm_logit_intercept will add what is equivalent to an intercept in a logistic regression. When coords 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
)

# Adding the intercept terms and a motif from tobacco to mj
term_defm_logit_intercept(mymodel)
term_defm_transition_formula(mymodel, "{y1, 0y2} > {y1, y2}")

# Inspecting the model
mymodel
#> Num. of Arrays       : 0
#> Support size         : -
#> Support size range   : -
#> Arrays in powerset   : 0
#> Transform. Fun.      : no
#> Model terms ( 4)    :
#>  - Logit intercept alcohol
#>  - Logit intercept tobacco
#>  - Logit intercept mj
#>  - Motif {tobacco⁺, mj⁻}⇨{tobacco⁺, mj⁺}
#> Model Y variables (3):
#>   0) alcohol
#>   1) tobacco
#>   2) mj