Compute Conditional Probability of Each Observed Outcome Given Each True Outcome, for Every Subject
pistar_compute.RdCompute Conditional Probability of Each Observed Outcome Given Each True Outcome, for Every Subject
Arguments
- gamma
A numeric matrix of regression parameters for the observed outcome mechanism,
Y* | Y(observed outcome, given the true outcome) ~Z(misclassification predictor matrix). Rows of the matrix correspond to parameters for theY* = 1observed outcome, with the dimensions ofZ. Columns of the matrix correspond to the true outcome categories \(j = 1, \dots,\)n_cat.- Z
A numeric design matrix.
- n
An integer value specifying the number of observations in the sample. This value should be equal to the number of rows of the design matrix,
Z.- n_cat
The number of categorical values that the true outcome,
Y, and the observed outcome,Y*can take.
Value
pistar_compute returns a matrix of conditional probabilities,
\(P(Y_i^* = k | Y_i = j, Z_i) = \frac{\text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}}{1 + \text{exp}\{\gamma_{kj0} + \gamma_{kjZ} Z_i\}}\)
for each of the \(i = 1, \dots,\) n subjects. Rows of the matrix
correspond to each subject and observed outcome. Specifically, the probability
for subject \(i\) and observed category $1$ occurs at row \(i\). The probability
for subject \(i\) and observed category $2$ occurs at row \(i +\) n.
Columns of the matrix correspond to the true outcome categories \(j = 1, \dots,\) n_cat.