# Estimated weights for missing data

### Description

Creates or adjusts a two-phase survey design object using a logistic regression model for second-phase sampling probability. This function should be particularly useful in reweighting to account for missing data.

### Usage

1 2 3 4 5 6 |

### Arguments

`data` |
twophase design object or data frame |

`formula` |
Predictors for estimating weights |

`working.model` |
Model fitted to complete (ie phase 1) data |

`subset` |
Subset of data frame with complete data (ie phase 1).
If |

`strata` |
Stratification (if any) of phase 2 sampling |

`...` |
for future expansion |

### Details

If `data`

is a data frame, `estWeights`

first creates a
two-phase design object. The `strata`

argument is used only to
compute finite population corrections, the same variables must be
included in `formula`

to compute stratified sampling probabilities.

With a two-phase design object, `estWeights`

estimates the sampling
probabilities using logistic regression as described by Robins et al
(1994) and adds information to the object to enable correct sandwich
standard errors to be computed.

An alternative to specifying `formula`

is to specify
`working.model`

. The estimating functions from this model will be
used as predictors of the sampling probabilities, which will increase
efficiency to the extent that the working model and the model of
interest estimate the same parameters (Kulich \& Lin 2004).

The effect on a two-phase design object is very similar to
`calibrate`

, and is identical when `formula`

specifies a saturated model.

### Value

A two-phase survey design object.

### References

Breslow NE, Lumley T, Ballantyne CM, Chambless LE, Kulich M. (2009) Using the Whole Cohort in the Analysis of Case-Cohort Data. Am J Epidemiol. 2009 Jun 1;169(11):1398-405.

Robins JM, Rotnitzky A, Zhao LP. (1994) Estimation of regression coefficients when some regressors are not always observed. Journal of the American Statistical Association, 89, 846-866.

Kulich M, Lin DY (2004). Improving the Efficiency of Relative-Risk Estimation in Case-Cohort Studies. Journal of the American Statistical Association, Vol. 99, pp.832-844

Lumley T, Shaw PA, Dai JY (2011) "Connections between survey calibration estimators and semiparametric models for incomplete data" International Statistical Review. 79:200-220. (with discussion 79:221-232)

### See Also

`postStratify`

,
`calibrate`

, `twophase`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
data(airquality)
## ignoring missingness, using model-based standard error
summary(lm(log(Ozone)~Temp+Wind, data=airquality))
## Without covariates to predict missingness we get
## same point estimates, but different (sandwich) standard errors
daq<-estWeights(airquality, formula=~1,subset=~I(!is.na(Ozone)))
summary(svyglm(log(Ozone)~Temp+Wind,design=daq))
## Reweighting based on weather, month
d2aq<-estWeights(airquality, formula=~Temp+Wind+Month,
subset=~I(!is.na(Ozone)))
summary(svyglm(log(Ozone)~Temp+Wind,design=d2aq))
``` |