Weights of the calibration estimator

Description

Calculates the calibration weights from a disjunct matrix of covariates, a vector of population totals and a vector of initial weights.

Usage

calib_weights(Xs, totals, initial_weights, N, ...)

Arguments

Details

The function uses the 'calib' function from the 'sampling' package for the estimation of g-weights, which are multiplied by the initial weights to obtain the final calibration weights. The initial weights can be calculated previously from the propensities for any of the implemented methods (see functions lee_weights, sc_weights, valliant_weights, vd_weights). The population size is used to scale said initial weights so they are easier to calibrate.

Value

A vector with the corresponding weights.

Examples

n = nrow(sampleNP)
N = 50000
language_total = 45429
covariates = c("education_primaria", "education_secundaria",
   "age", "sex")
pi = propensities(sampleNP, sampleP, covariates, algorithm = "glm", smooth = FALSE)
wi = sc_weights(pi$convenience)
calib_weights(sampleNP$language, language_total, wi, N, method = "raking")

Confidence interval

Description

Calculates the confidence interval for the estimator considered.

Usage

confidence_interval(estimation, std_dev, confidence = 0.95)

Arguments

Value

A vector containing the lower and upper bounds.

Examples

covariates = c("education_primaria","education_secundaria",
"age", "sex")
pi = propensities(sampleNP, sampleP, covariates, algorithm = "glm", smooth = FALSE)
psa_weights = sc_weights(pi$convenience)
N = 50000
Y_est = total_estimation(sampleNP, psa_weights, estimated_vars = "vote_pens", N = N)
VY_est = fast_jackknife_variance(sampleNP, psa_weights,
   estimated_vars = "vote_pens") * N^2
confidence_interval(Y_est, sqrt(VY_est), confidence = 0.90)

Calculates Jackknife variance without reweighting

Description

Calculates the variance of a given estimator by Leave-One-Out Jackknife (Quenouille, 1956) with the original adjusted weights.

Usage

fast_jackknife_variance(sample, weights, estimated_vars, N = NULL)

Arguments

Details

The variance estimation is performed by eliminating an individual at each iteration with its corresponding weight and estimating the mean of the corresponding subsample, which is further used in the Jackknife formula as the usual procedure. The calculation of variance estimates through this procedure might take less computation time but also might not take into account the variance of the weighting method.

Value

A vector containing the resulting variance for each variable.

References

Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43(3/4), 353-360.

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
psa_weights = sc_weights(data_propensities$convenience)
fast_jackknife_variance(sampleNP, psa_weights, c("vote_pens"), 50000)

Calculates Jackknife variance with reweighting for an arbitrary estimator

Description

Calculates the variance of a given estimator by Leave-One-Out Jackknife (Quenouille, 1956) with reweighting in each iteration.

Usage

generic_jackknife_variance(sample, estimator, N = NULL)

Arguments

Details

The estimation of the variance requires a recalculation of the estimates in each iteration which might involve weighting adjustments, leading to an increase in computation time. It is expected that the estimated variance captures the weighting adjustments' variability and the estimator's variability.

Value

The resulting variance.

References

Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43(3/4), 353-360.

Examples

covariates = c("education_primaria", "education_secundaria",
   "age", "sex", "language")
if (is.numeric(sampleNP$vote_gen))
   sampleNP$vote_gen = factor(sampleNP$vote_gen, c(0, 1), c('F', 'T'))
vote_gen_estimator = function(sample) {
   model_based(sample, population, covariates,
      "vote_gen", positive_label = 'T', algorithm = 'glmnet')
}
generic_jackknife_variance(sampleNP, vote_gen_estimator)

Calculates Jackknife variance with reweighting for PSA

Description

Calculates the variance of PSA by Leave-One-Out Jackknife (Quenouille, 1956) with reweighting in each iteration.

Usage

jackknife_variance(
  estimated_vars,
  convenience_sample,
  reference_sample,
  covariates,
  N = NULL,
  algorithm = "glm",
  smooth = FALSE,
  proc = NULL,
  trControl = trainControl(classProbs = TRUE),
  weighting.func = "sc",
  g = 5,
  calib = FALSE,
  calib_vars = NULL,
  totals = NULL,
  args.calib = NULL,
  ...
)

Arguments

Details

The estimation of the variance requires a recalculation of the estimates in each iteration which might involve weighting adjustments, leading to an increase in computation time. It is expected that the estimated variance captures the weighting adjustments' variability and the estimator's variability.

Value

The resulting variance.

References

Quenouille, M. H. (1956). Notes on bias in estimation. Biometrika, 43(3/4), 353-360.

Examples

#A simple example without calibration and default parameters
covariates = c("education_primaria", "education_secundaria")
jackknife_variance("vote_pens",sampleNP, sampleP, covariates)

#An example with linear calibration and default parameters
covariates = c("education_primaria", "education_secundaria")
calib_vars = c("age", "sex")
totals = c(2544377, 24284)

jackknife_variance("vote_pens",sampleNP, sampleP, covariates,
calib = T, calib_vars, totals, args.calib = list(method = "linear"))

Calculates Lee weights

Description

Computes weights from propensity estimates using the propensity stratification design weights averaging formula introduced in Lee (2006) and Lee and Valliant (2009).

Usage

lee_weights(convenience_propensities, reference_propensities, g = 5)

Arguments

Details

The function takes the vector of propensities \pi(x) and calculates the weights to be applied in the Horvitz-Thompson estimator using the formula that can be found in Lee (2006) and Lee and Valliant (2009). The vector of propensities is divided in g strata (ideally five according to Cochran, 1968) aiming to have individuals with similar propensities in each strata. After the stratification, weight is calculated as follows for an individual i:

w_i = \frac{n_r(g_i) / n_r}{n_v(g_i) / n_v}

where g_i represents the strata to which i belongs, n_r (g_i) and n_v (g_i) are the number of individuals in the g_i strata from the reference and the convenience sample respectively, and n_r and n_v are the sample sizes for the reference and the convenience sample respectively.

Value

A vector with the corresponding weights.

References

Lee, S. (2006). Propensity score adjustment as a weighting scheme for volunteer panel web surveys. Journal of official statistics, 22(2), 329.

Lee, S., & Valliant, R. (2009). Estimation for volunteer panel web surveys using propensity score adjustment and calibration adjustment. Sociological Methods & Research, 37(3), 319-343.

Cochran, W. G. (1968). The Effectiveness of Adjustment by Subclassification in Removing Bias in Observational Studies. Biometrics, 24(2), 295-313

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
lee_weights(data_propensities$convenience, data_propensities$reference)

Predicts unknown responses by matching

Description

It uses the matching method introduced by Rivers (2007). The idea is to model the relationship between y_k and x_k using the convenience sample in order to predict y_k for the reference sample. You can then predict the total using the 'total_estimation' method.

Usage

matching(
  convenience_sample,
  reference_sample,
  covariates,
  estimated_var,
  positive_label = NULL,
  algorithm = "glm",
  proc = NULL,
  ...
)

Arguments

Details

Training of the models is done via the 'caret' package. The algorithm specified in algorithm must match one of the names in the list of algorithms supported by 'caret'. If the estimated variable is categorical, probabilities are returned.

Value

A vector containing the estimated responses for the reference sample.

References

Rivers, D. (2007). Sampling for Web Surveys. Presented in Joint Statistical Meetings, Salt Lake City, UT.

Examples

#Simple example with default parameters
N = 50000
covariates = c("education_primaria", "education_secundaria")
if (is.numeric(sampleNP$vote_gen))
   sampleNP$vote_gen = factor(sampleNP$vote_gen, c(0, 1), c('F', 'T'))
estimated_votes = data.frame(
   vote_gen = matching(sampleNP, sampleP, covariates, "vote_gen", 'T')
)
total_estimation(estimated_votes, N / nrow(estimated_votes), c("vote_gen"), N)

Estimates the population means

Description

Estimates the means for the specified variables measured in a sample given some pre-calculated weights.

Usage

mean_estimation(sample, weights, estimated_vars, N = NULL)

Arguments

Value

A vector with the corresponding estimations.

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
psa_weights = sc_weights(data_propensities$convenience)
mean_estimation(sampleNP, psa_weights, c("vote_pens"))

Calculates a model assisted estimation

Description

It uses the model assisted estimator introduced by Särndal et al. (1992).

Usage

model_assisted(
  sample_data,
  weights,
  full_data,
  covariates,
  estimated_var,
  estimate_mean = FALSE,
  positive_label = NULL,
  algorithm = "glm",
  proc = NULL,
  ...
)

Arguments

Details

Training of the models is done via the 'caret' package. The algorithm specified in algorithm must match one of the names in the list of algorithms supported by 'caret'.

Value

The population total estimation (or mean if specified by the 'estimate_mean' parameter).

References

Särndal, C. E., Swensson, B., & Wretman, J. (1992). Model assisted survey sampling. Springer, New York.

Examples

#Simple example
covariates = c("education_primaria", "education_secundaria",
   "age", "sex", "language")
if (is.numeric(sampleNP$vote_gen))
   sampleNP$vote_gen = factor(sampleNP$vote_gen, c(0, 1), c('F', 'T'))
model_assisted(sampleNP, nrow(population) / nrow(sampleNP),
   population, covariates, "vote_gen", positive_label = 'T', algorithm = 'glmnet')

Calculates a model based estimation

Description

It uses the model based estimator. The idea in order to estimate the population total is to add the sample responses and the predicted responses for the individuals not contained in the sample. See for example Valliant et al. (2000).

Usage

model_based(
  sample_data,
  full_data,
  covariates,
  estimated_var,
  estimate_mean = FALSE,
  positive_label = NULL,
  algorithm = "glm",
  proc = NULL,
  ...
)

Arguments

Details

Training of the models is done via the 'caret' package. The algorithm specified in algorithm must match one of the names in the list of algorithms supported by 'caret'.

Value

The population total estimation (or mean if specified by the 'estimate_mean' parameter).

References

Valliant, R., Dorfman, A. H., & Royall, R. M. (2000) Finite population sampling and inference: a prediction approach. Wiley, New York.

Examples

#Simple example
covariates = c("education_primaria", "education_secundaria",
   "age", "sex", "language")
if (is.numeric(sampleNP$vote_gen))
   sampleNP$vote_gen = factor(sampleNP$vote_gen, c(0, 1), c('F', 'T'))
model_based(sampleNP, population, covariates,
   "vote_gen", positive_label = 'T', algorithm = 'glmnet')

Calculates a model calibrated estimation

Description

It uses the model calibrated estimator introduced by Wu et al. (2001).

Usage

model_calibrated(
  sample_data,
  weights,
  full_data,
  covariates,
  estimated_var,
  estimate_mean = FALSE,
  positive_label = NULL,
  algorithm = "glm",
  proc = NULL,
  ...
)

Arguments

Details

Training of the models is done via the 'caret' package. The algorithm specified in algorithm must match one of the names in the list of algorithms supported by 'caret'.

Value

The population total estimation (or mean if specified by the 'estimate_mean' parameter).

References

Wu, C., & Sitter, R. R. (2001). A model-calibration approach to using complete auxiliary information from survey data. Journal of the American Statistical Association, 96(453), 185-193.

Examples

#Simple example
covariates = c("education_primaria", "education_secundaria",
   "age", "sex", "language")
if (is.numeric(sampleNP$vote_gen))
   sampleNP$vote_gen = factor(sampleNP$vote_gen, c(0, 1), c('F', 'T'))
model_calibrated(sampleNP, nrow(population) / nrow(sampleNP),
   population, covariates, "vote_gen", positive_label = 'T', algorithm = 'glmnet')

A full population

Description

A dataset of a simulated fictitious population of 50,000 individuals. Further details on the generation of the dataset can be found in Ferri-García and Rueda (2018). The variables present in the dataset are the following:

• education_primaria. A binary variable indicating if the highest academic level achieved by the individual is Primary Education.

• education_secundaria. A binary variable indicating if the highest academic level achieved by the individual is Secondary Education.

• education_terciaria. A binary variable indicating if the highest academic level achieved by the individual is Tertiary Education.

• age. A numeric variable, with values ranging from 18 to 100, indicating the age of the individual.

• sex. A binary variable indicating if the individual is a man.

• language. A binary variable indicating if the individual is a native.

Usage

population

Format

An object of class data.frame with 50000 rows and 6 columns.

References

Ferri-García, R., & Rueda, M. (2018). Efficiency of propensity score adjustment and calibration on the estimation from non-probabilistic online surveys. SORT-Statistics and Operations Research Transactions, 1(2), 159-162.

Estimates the population proportion

Description

Estimates the proportion of a given class or classes for the specified variables measured in a sample given some pre-calculated weights.

Usage

prop_estimation(sample, weights, estimated_vars, class, N = NULL)

Arguments

Value

A vector with the corresponding estimations.

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
psa_weights = sc_weights(data_propensities$convenience)

#The function will estimate the proportion of individuals
#with the 0 value in vote_pens and the 1 value in vote_pir
prop_estimation(sampleNP, psa_weights, c("vote_pens", "vote_pir"), c(0, 1))

Calculates sample propensities

Description

Given a convenience sample and a reference sample, computes estimates on the propensity to participate in the convenience sample based on classification models to be selected by the user.

Usage

propensities(
  convenience_sample,
  reference_sample,
  covariates,
  algorithm = "glm",
  smooth = FALSE,
  proc = NULL,
  trControl = trainControl(classProbs = TRUE),
  ...
)

Arguments

Details

Training of the propensity estimation models is done via the 'caret' package. The algorithm specified in algorithm must match one of the names in the list of algorithms supported by 'caret'. Case weights are used to balance classes (for models that accept them). The smoothing formula for propensities avoids mathematical irregularities in the calculation of sample weight when an estimated propensity is 0 or 1. Further details can be found in Buskirk and Kolenikov (2015).

Value

A list containing 'convenience' propensities and 'reference' propensities.

References

Buskirk, T. D., & Kolenikov, S. (2015). Finding respondents in the forest: A comparison of logistic regression and random forest models for response propensity weighting and stratification. Survey Methods: Insights from the Field, 17.

Examples

#Simple example with default parameters
covariates = c("education_primaria", "education_secundaria")
propensities(sampleNP, sampleP, covariates)

A non-probabilistic sample

Description

A dataset of 1000 individuals extracted from the subpopulation of individuals with internet access in a simulated fictitious population of 50,000 individuals. This sample attempts to reproduce a case of nonprobability sampling with selection bias, as there are important differences between the potentially covered population, the covered population and the full target population. Further details on the generation of the dataset can be found in Ferri-García and Rueda (2018). The variables present in the dataset are the following:

• vote_gen. A binary variable indicating if the individual vote preferences are for Party 1. This variable is related to gender.

• vote_pens. A binary variable indicating if the individual vote preferences are for Party 2. This variable is related to age.

• vote_pir. A binary variable indicating if the individual vote preferences are for Party 3. This variable is related to age and internet access.

• education_primaria. A binary variable indicating if the highest academic level achieved by the individual is Primary Education.

• education_secundaria. A binary variable indicating if the highest academic level achieved by the individual is Secondary Education.

• education_terciaria. A binary variable indicating if the highest academic level achieved by the individual is Tertiary Education.

• age. A numeric variable, with values ranging from 18 to 100, indicating the age of the individual.

• sex. A binary variable indicating if the individual is a man.

• language. A binary variable indicating if the individual is a native.

Usage

sampleNP

Format

An object of class data.frame with 1000 rows and 9 columns.

References

Ferri-García, R., & Rueda, M. (2018). Efficiency of propensity score adjustment and calibration on the estimation from non-probabilistic online surveys. SORT-Statistics and Operations Research Transactions, 1(2), 159-162.

A probabilistic sample

Description

A dataset of 500 individuals extracted with simple random sampling from a simulated fictitious population of 50,000 individuals. Further details on the generation of the dataset can be found in Ferri-García and Rueda (2018). The variables present in the dataset are the following:

• education_primaria. A binary variable indicating if the highest academic level achieved by the individual is Primary Education.

• education_secundaria. A binary variable indicating if the highest academic level achieved by the individual is Secondary Education.

• education_terciaria. A binary variable indicating if the highest academic level achieved by the individual is Tertiary Education.

• age. A numeric variable, with values ranging from 18 to 100, indicating the age of the individual.

• sex. A binary variable indicating if the individual is a man.

Usage

sampleP

Format

An object of class data.frame with 500 rows and 5 columns.

References

Ferri-García, R., & Rueda, M. (2018). Efficiency of propensity score adjustment and calibration on the estimation from non-probabilistic online surveys. SORT-Statistics and Operations Research Transactions, 1(2), 159-162.

Calculates Schonlau and Couper weights

Description

Computes weights from propensity estimates using the (1 - pi_i)/pi_i formula introduced in Schonlau and Couper (2017).

Usage

sc_weights(propensities)

Arguments

Details

The function takes the vector of propensities \pi(x) and calculates the weights to be applied in the Hajek estimator using the formula that can be found in Schonlau and Couper (2017). For an individual i, weight is calculated as follows:

w_i = \frac{1 - \pi_i (x)}{\pi_i (x)}

Value

A vector with the corresponding weights.

References

Schonlau, M., & Couper, M. P. (2017). Options for conducting web surveys. Statistical Science, 32(2), 279-292.

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
sc_weights(data_propensities$convenience)

Estimates the population totals

Description

Estimates the population totals for the specified variables measured in a sample given some pre-calculated weights.

Usage

total_estimation(sample, weights, estimated_vars, N)

Arguments

Value

A vector with the corresponding estimations.

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
psa_weights = sc_weights(data_propensities$convenience)
total_estimation(sampleNP, psa_weights, c("vote_pens"), 50000)

Calculates Valliant weights

Description

Computes weights from propensity estimates using the 1/pi_i formula introduced in Valliant (2019).

Usage

valliant_weights(propensities)

Arguments

Details

The function takes the vector of propensities \pi(x) and calculates the weights to be applied in the Hajek estimator using the formula that can be found in Valliant (2019). For an individual i, weight is calculated as follows:

w_i = 1/\pi_i (x)

Value

A vector with the corresponding weights.

References

Valliant, R. (2019). Comparing Alternatives for Estimation from Nonprobability Samples. Journal of Survey Statistics and Methodology, smz003, https://doi.org/10.1093/jssam/smz003

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
valliant_weights(data_propensities$convenience)

Calculates Valliant and Dever weights

Description

Computes weights from propensity estimates using the propensity stratification 1/p_i averaging formula introduced in Valliant and Dever (2011).

Usage

vd_weights(convenience_propensities, reference_propensities, g = 5)

Arguments

Details

The function takes the vector of propensities \pi(x) and calculates the weights to be applied in the Horvitz-Thompson estimator using the formula that can be found in Valliant and Dever (2019). The vector of propensities is divided in g strata (ideally five according to Cochran, 1968) aiming to have individuals with similar propensities in each strata. After the stratification, weight is calculated as follows for an individual i:

w_i = \frac{n(g_i)}{ \sum_{k \in g_i} \pi_k (x)}

where g_i represents the strata to which i belongs, and n(g_i) is the number of individuals in the g_i strata.

Value

A vector with the corresponding weights.

References

Valliant, R., & Dever, J. A. (2011). Estimating propensity adjustments for volunteer web surveys. Sociological Methods & Research, 40(1), 105-137.

Cochran, W. G. (1968). The Effectiveness of Adjustment by Subclassification in Removing Bias in Observational Studies. Biometrics, 24(2), 295-313

Examples

covariates = c("education_primaria", "education_secundaria")
data_propensities = propensities(sampleNP, sampleP, covariates)
vd_weights(data_propensities$convenience, data_propensities$reference)