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@LukaszChrostowski
LukaszChrostowski committed Dec 2, 2023
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304 changes: 258 additions & 46 deletions README.Rmd
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Expand Up @@ -80,19 +80,19 @@ remotes::install_github("ncn-foreigners/nonprobsvy@dev")
## Basic idea

Consider the following setting where two samples are available:
non-probability (denoted as $S_A$) and probability (denoted as $S_B$)
non-probability (denoted as $S_A$ ) and probability (denoted as $S_B$)
where set of auxiliary variables (denoted as $\boldsymbol{X}$) is
available for both sources while $Y$ and $\boldsymbol{d}$ (or
$\boldsymbol{w}$) is present only in probability sample.

| Sample | | Auxiliary variables $\bol dsymbol{X}$ | Target variable $Y$ | Design ($\bold symbol{d}$) or calibrated ($\bold symbol{w}$) weights |
| Sample | | Auxiliary variables $\boldsymbol{X}$ | Target variable $Y$ | Design ($\boldsymbol{d}$) or calibrated ($\boldsymbol{w}$) weights |
|---------------|--------------:|:-------------:|:-------------:|:-------------:|
| $S_A$ (non-p robability) | 1 | \$ \checkmark\$ | \$ \checkmark\$ | ? |
| | ... | \$ \checkmark\$ | \$ \checkmark\$ | ? |
| | $n_A$ | \$ \checkmark\$ | \$ \checkmark\$ | ? |
| $S_B$ (p robability) | $n_A+1$ | \$ \checkmark\$ | ? | \$ \checkmark\$ |
| | ... | \$ \checkmark\$ | ? | \$ \checkmark\$ |
| | $n_A+n_B$ | \$ \checkmark\$ | ? | \$ \checkmark\$ |
| $S_A$ (non-probability) | 1 | $\checkmark$ | $\checkmark$ | ? |
| | ... | $\checkmark$ | $\checkmark$ | ? |
| | $n_A$ | $\checkmark$ | $\checkmark$ | ? |
| $S_B$ (probability) | $n_A+1$ | $\checkmark$ | ? | $\checkmark$ |
| | ... | $\checkmark$ | ? | $\checkmark$ |
| | $n_A+n_B$ | $\checkmark$ | ? | $\checkmark$ |

## Basic functionalities

Expand All @@ -104,12 +104,12 @@ $(y_k, \boldsymbol{x}_k, R_k)$, we can approach this problem with the
possible scenarios:

- unit-level data is available for the non-probability sample $S_{A}$,
i.e. \(y_{k}, \boldsymbol{x}_{k}\) is available for all units
\(k \in S_{A}\), and population-level data is available for
\(\boldsymbol{x}_{1}, ..., \boldsymbol{x}_{p}\), denoted as
$\tau_{x_{1}}, \tau_{x_{2}}, ..., \tau_{x_{p}}$ and population size
$N$ is known. We can also consider situations where population data
are estimated (e.g. on the basis of a survey to which we do not have
i.e. $(y_{k}, \boldsymbol{x}_{k})$ is available for all units
$k \in S_{A}$, and population-level data is available for
$\boldsymbol{x}_{1}, ..., \boldsymbol{x}_{p}$, denoted as
$\tau_{x_{1}}, \tau_{x_{2}}, ..., \tau_{x_{p}}$ and population size $N$ is
known. We can also consider situations where population data are
estimated (e.g. on the basis of a survey to which we do not have
access),
- unit-level data is available for the non-probability sample $S_A$
and the probability sample $S_B$, i.e.
Expand All @@ -120,41 +120,253 @@ possible scenarios:

### When unit-level data is available for non-probability survey only

| Estimator | Example code |
|------------------------------------|------------------------------------|
| | |
| Mass imputation based on regression imputation | \`\`\`{r, eval = FALSE} nonprob( outcome = y \~ x1 + x2 + \... + xk, data = nonprob, pop_totals = c(\`(Intercept)\`= N, x1 = tau_x1, x2 = tau_x2, \..., xk = tau_xk), method_outcome = "glm", family_outcome = "gaussian" ) \`\`\` |
| | |
| Inverse probability weighting | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, target = \~ y, data = nonprob, pop_totals = c(\`(Intercept)\` = N, x1 = tau_x1, x2 = tau_x2, \..., xk = tau_xk), method_selection = "logit" ) \`\`\` |
| | |
| Inverse probability weighting with calibration constraint | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, target = \~ y, data = nonprob, pop_totals = c(\`(Intercept)\`= N, x1 = tau_x1, x2 = tau_x2, \..., xk = tau_xk), method_selection = "logit", control_selection = controlSel(est_method_sel = "gee", h = 1) ) \`\`\` |
| | |
| Doubly robust estimator | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, outcome = y \~ x1 + x2 + ..., + xk, pop_totals = c(\`(Intercept)\` = N, x1 = tau_x1, x2 = tau_x2, \..., xk = tau_xk), svydesign = prob, method_outcome = "glm", family_outcome = "gaussian" ) \`\`\` |
| | |
<table class='table'>
<tr> <th>Estimator</th> <th>Example code</th> <tr>
<tr>
<td>
Mass imputation based on regression imputation
</td>
<td>
```{r, eval = FALSE}
nonprob(
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
pop_totals = c(`(Intercept)`= N,
x1 = tau_x1,
x2 = tau_x2,
...,
xk = tau_xk),
method_outcome = "glm",
family_outcome = "gaussian"
)
```
</td>
<tr>
<tr>
<td>
Inverse probability weighting
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
target = ~ y,
data = nonprob,
pop_totals = c(`(Intercept)` = N,
x1 = tau_x1,
x2 = tau_x2,
...,
xk = tau_xk),
method_selection = "logit"
)
```
</td>
<tr>
<tr>
<td>
Inverse probability weighting with calibration constraint
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
target = ~ y,
data = nonprob,
pop_totals = c(`(Intercept)`= N,
x1 = tau_x1,
x2 = tau_x2,
...,
xk = tau_xk),
method_selection = "logit",
control_selection = controlSel(est_method_sel = "gee", h = 1)
)
```
</td>
<tr>
<tr>
<td>
Doubly robust estimator
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
outcome = y ~ x1 + x2 + …, + xk,
pop_totals = c(`(Intercept)` = N,
x1 = tau_x1,
x2 = tau_x2,
...,
xk = tau_xk),
svydesign = prob,
method_outcome = "glm",
family_outcome = "gaussian"
)
```
</td>
<tr>
</table>

### When unit-level data are available for both surveys

| Estimator | Example code |
|------------------------------------|------------------------------------|
| | |
| Mass imputation based on regression imputation | \`\`\`{r, eval = FALSE} nonprob( outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "glm", family_outcome = "gaussian" ) \`\`\` |
| | |
| Mass imputation based on nearest neighbour imputation | \`\`\`{r, eval = FALSE} nonprob( outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "nn", family_outcome = "gaussian", control_outcome = controlOutcome(k = 2) ) \`\`\` |
| | |
| Mass imputation based on predictive mean matching | \`\`\`{r, eval = FALSE} nonprob( outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "pmm", family_outcome = "gaussian" ) \`\`\` |
| | |
| Mass imputation based on regression imputation with variable selection (LASSO) | \`\`\`{r, eval = FALSE} nonprob( outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "pmm", family_outcome = "gaussian", control_outcome = controlOut(penalty = "lasso"), control_inference = controlInf(vars_selection = TRUE) ) \`\`\` |
| | |
| Inverse probability weighting | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, target = \~ y, data = nonprob, svydesign = prob, method_selection = "logit" ) \`\`\` |
| | |
| Inverse probability weighting with calibration constraint | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, target = \~ y, data = nonprob, svydesign = prob, method_selection = "logit", control_selection = controlSel(est_method_sel = "gee", h = 1) ) \`\`\` |
| | |
| Inverse probability weighting with calibration constraint with variable selection (SCAD) | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, target = \~ y, data = nonprob, svydesign = prob, method_outcome = "pmm", family_outcome = "gaussian", control_inference = controlInf(vars_selection = TRUE) ) \`\`\` |
| | |
| Doubly robust estimator | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "glm", family_outcome = "gaussian" ) \`\`\` |
| | |
| Doubly robust estimator with variable selection (SCAD) and bias minimization | \`\`\`{r, eval = FALSE} nonprob( selection = \~ x1 + x2 + \... + xk, outcome = y \~ x1 + x2 + \... + xk, data = nonprob, svydesign = prob, method_outcome = "glm", family_outcome = "gaussian", control_inference = controlInf( vars_selection = TRUE, bias_correction = TRUE ) ) \`\`\` |
| | |
<table class='table'>
<tr> <th>Estimator</th> <th>Example code</th> <tr>
<tr>
<td>
Mass imputation based on regression imputation
</td>
<td>
```{r, eval = FALSE}
nonprob(
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "glm",
family_outcome = "gaussian"
)
```
</td>
<tr>
<tr>
<td>
Mass imputation based on nearest neighbour imputation
</td>
<td>
```{r, eval = FALSE}
nonprob(
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "nn",
family_outcome = "gaussian",
control_outcome = controlOutcome(k = 2)
)
```
</td>
<tr>
<tr>
<td>
Mass imputation based on predictive mean matching
</td>
<td>
```{r, eval = FALSE}
nonprob(
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "pmm",
family_outcome = "gaussian"
)
```
</td>
<tr>
<tr>
<td>
Mass imputation based on regression imputation with variable selection (LASSO)
</td>
<td>
```{r, eval = FALSE}
nonprob(
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "pmm",
family_outcome = "gaussian",
control_outcome = controlOut(penalty = "lasso"),
control_inference = controlInf(vars_selection = TRUE)
)
```
</td>
<tr>
<tr>
<td>
Inverse probability weighting
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
target = ~ y,
data = nonprob,
svydesign = prob,
method_selection = "logit"
)
```
</td>
<tr>
<tr>
<td>
Inverse probability weighting with calibration constraint
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
target = ~ y,
data = nonprob,
svydesign = prob,
method_selection = "logit",
control_selection = controlSel(est_method_sel = "gee", h = 1)
)
```
</td>
<tr>
<tr>
<td>
Inverse probability weighting with calibration constraint with variable selection (SCAD)
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
target = ~ y,
data = nonprob,
svydesign = prob,
method_outcome = "pmm",
family_outcome = "gaussian",
control_inference = controlInf(vars_selection = TRUE)
)
```
</td>
<tr>
<tr>
<td>
Doubly robust estimator
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "glm",
family_outcome = "gaussian"
)
```
</td>
<tr>
<tr>
<td>
Doubly robust estimator with variable selection (SCAD) and bias minimization
</td>
<td>
```{r, eval = FALSE}
nonprob(
selection = ~ x1 + x2 + ... + xk,
outcome = y ~ x1 + x2 + ... + xk,
data = nonprob,
svydesign = prob,
method_outcome = "glm",
family_outcome = "gaussian",
control_inference = controlInf(
vars_selection = TRUE,
bias_correction = TRUE
)
)
```
</td>
<tr>
</table>

## Examples

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