# Builds condition probability matrices for Horvitz-Thompson estimation from randomizr declaration

Builds condition probability matrices for Horvitz-Thompson estimation from randomizr declaration

declaration_to_condition_pr_mat(ra_declaration, condition1 = NULL, condition2 = NULL, prob_matrix = NULL)

## Arguments

ra_declaration | An object of class |
---|---|

condition1 | The name of the first condition, often the control group. If |

condition2 | The name of the second condition, often the treatment group. If |

prob_matrix | An optional probability matrix to override the one in `ra_declaration` |

## Value

a numeric 2n*2n matrix of marginal and joint condition treatment
probabilities to be passed to the `condition_pr_mat`

argument of
`horvitz_thompson`

. See details.

## Details

This function takes a `"ra_declaration"`

, generated
by the `declare_ra`

function in randomizr and
returns a 2n*2n matrix that can be used to fully specify the design for
`horvitz_thompson`

estimation. This is done by passing this
matrix to the `condition_pr_mat`

argument of
`horvitz_thompson`

.

Currently, this function can learn the condition probability matrix for a wide variety of randomizations: simple, complete, simple clustered, complete clustered, blocked, block-clustered.

A condition probability matrix is made up of four submatrices, each of which corresponds to the joint and marginal probability that each observation is in one of the two treatment conditions.

The upper-left quadrant is an n*n matrix. On the diagonal is the marginal probability of being in condition 1, often control, for every unit (Pr(Z_i = Condition1) where Z represents the vector of treatment conditions). The off-diagonal elements are the joint probabilities of each unit being in condition 1 with each other unit, Pr(Z_i = Condition1, Z_j = Condition1) where i indexes the rows and j indexes the columns.

The upper-right quadrant is also an n*n matrix. On the diagonal is the joint probability of a unit being in condition 1 and condition 2, often the treatment, and thus is always 0. The off-diagonal elements are the joint probability of unit i being in condition 1 and unit j being in condition 2, Pr(Z_i = Condition1, Z_j = Condition2).

The lower-left quadrant is also an n*n matrix. On the diagonal is the joint probability of a unit being in condition 1 and condition 2, and thus is always 0. The off-diagonal elements are the joint probability of unit i being in condition 2 and unit j being in condition 1, Pr(Z_i = Condition2, Z_j = Condition1).

The lower-right quadrant is an n*n matrix. On the diagonal is the marginal probability of being in condition 2, often treatment, for every unit (Pr(Z_i = Condition2)). The off-diagonal elements are the joint probability of each unit being in condition 2 together, Pr(Z_i = Condition2, Z_j = Condition2).

## See also

`permutations_to_condition_pr_mat`

## Examples

# Learn condition probability matrix from complete blocked design library(randomizr) n <- 100 dat <- data.frame( blocks = sample(letters[1:10], size = n, replace = TRUE), y = rnorm(n) ) # Declare complete blocked randomization bl_declaration <- declare_ra(blocks = dat$blocks, prob = 0.4, simple = FALSE) # Get probabilities block_pr_mat <- declaration_to_condition_pr_mat(bl_declaration, 0, 1) # Do randomiztion dat$z <- conduct_ra(bl_declaration) horvitz_thompson(y ~ z, data = dat, condition_pr_mat = block_pr_mat)#> Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF #> z 0.0789944 0.2167921 0.3643785 0.7155754 -0.3459104 0.5038992 NA# When you pass a declaration to horvitz_thompson, this function is called # Equivalent to above call horvitz_thompson(y ~ z, data = dat, ra_declaration = bl_declaration)#> Estimate Std. Error t value Pr(>|t|) CI Lower CI Upper DF #> z 0.0789944 0.2167921 0.3643785 0.7155754 -0.3459104 0.5038992 NA