q_delta_f {COMBO} | R Documentation |

## M-Step Expected Log-Likelihood with respect to Delta

### Description

Objective function of the form:
`Q_{\delta} = \sum_{i = 1}^N \Bigl[\sum_{j = 1}^2 \sum_{k = 1}^2 \sum_{\ell = 1}^2 w_{ij} y^*_{ik} \tilde{y}_{i \ell} \text{log} \{ \tilde{\pi}_{i \ell kj} \}\Bigr]`

.
Used to obtain estimates of `\delta`

parameters.

### Usage

```
q_delta_f(
delta_v,
V,
obs_Ystar_matrix,
obs_Ytilde_matrix,
w_mat,
sample_size,
n_cat
)
```

### Arguments

`delta_v` |
A numeric array of regression parameters for the second-stage observed
outcome mechanism, |

`V` |
A numeric design matrix. |

`obs_Ystar_matrix` |
A numeric matrix of indicator variables (0, 1) for the observed
outcome |

`obs_Ytilde_matrix` |
A numeric matrix of indicator variables (0, 1) for the observed
outcome |

`w_mat` |
Matrix of E-step weights obtained from |

`sample_size` |
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, |

`n_cat` |
The number of categorical values that the true outcome, |

### Value

`q_beta_f`

returns the negative value of the expected log-likelihood function,
`Q_{\delta} = \sum_{i = 1}^N \Bigl[\sum_{j = 1}^2 \sum_{k = 1}^2 \sum_{\ell = 1}^2 w_{ij} y^*_{ik} \tilde{y}_{i \ell} \text{log} \{ \tilde{\pi}_{i \ell kj} \}\Bigr]`

,
at the provided inputs.

*COMBO*version 1.1.0 Index]