Determines if State Matrix is Degenerate for Given Data Set.

degeneracy_check finds indices for non-identifiable elements of state matrix and then flips values for those elements and checks changes in resulting fitness.

degeneracy_check(state_mat, action_vec, cols, data, outcome)

Arguments

state_mat	Numeric matrix with rows as states and columns as predictors.
action_vec	Numeric vector indicating what action to take for each state.
cols	Optional numeric vector same length as number of columns of the state matrix (state_mat) with the action that each column of the state matrix corresponds to the decision model taking in the previous period. This is only relevant when the predictor variables of the FSM are lagged outcomes that include the previous actions taken by that decision model.
data	Numeric matrix that has first col period and rest of cols are predictors.
outcome	Numeric vector same length as the number of rows as data.

Value

Returns a list of with sparse and corrected state matrix. If the model is fine, then
sparse_state_mat and corrected_state_mat should be equal to state_mat.

Details

degeneracy_check finds indices for non-identifiable elements of state matrix and then flips values for those elements and checks changes in resulting fitness. Being in state/row k (e.g. 2) corresponds to taking action j (e.g. D). For row k, all entries in the matrix that corresponds to taking action j last period (e.g. columns 2 and 4 for D) are identifiable; however, columns that correspond to not taking action j last period (e.g. columns 1 and 3 for D) for the row $k$ that corresponds to taking action j are not identifiable for a deterministic play of the strategy. For all elements of the matrix that are not identifiable, the value of the element can be any integer in the inclusive range of the number of rows of the matrix (e.g. 1 or 2). With empirical data, where the probability that a single deterministic model generated the data is effectively zero, it is useful to find every entry in the matrix that would be unidentifiable if the strategy were played deterministically and then for each element flip it to its opposite value and test for any change in fitness of the strategy on the data. This function implements this idea. If there is no change, a sparse matrix is returned where the the elements in that matrix with a 0 are unidentifiable because their value makes no difference to the fit of the strategy to the provided data. If, for each element in the matrix, switching its value led to a decrease in fitness the following message is displayed, ``Your strategy is a deterministic approximation of a stochastic process and all of the elements of the state matrix can be identified.'' If the model is fine, then sparse_state_mat and corrected_state_mat should be equal to state_mat.