Estimation

RDS Tools package has 4 estimation functions: (1) RDSmean, (2) RDStable, (3) RDSlm, (4) RDSglm. Users can control the use of weights, selection of variance estimation, as well as the number of resamples if one of the variance estimation resampling approaches is used. Note, before using the estimation functions, please make sure that you preprocess data with RDSdata function.

RDSmean - Descriptive Statistics

Estimating mean with respondent driven sampling sample data. This function calculates weighted or unweighted means for either a continuous or a categorical variable. For continuous variables, it returns a single mean and standard error. For categorical variables, it returns one proportion and standard error per level. Standard errors are calculated using naive (delta-method) or resampling approaches from ‘RDSboot’.

Usage

RDSmean(x, data, weight=None, var_est=None, resample_n=None, n_cores=None, na_rm=True, return_bootstrap_means=False, return_node_counts=False)

Arguments

x: str. A variable of interest. Continuous variables (numeric dtypes) return a single mean and SE. Categorical variables (object, string, bool, or pandas Categorical dtypes) return one proportion and SE per level. Note that integer-coded categoricals such as Race=1,2,3 are treated as numeric by default; convert them with data[col] = data[col].astype('category') before calling RDSmean to get per-category output.
data: pandas.DataFrame. The output DataFrame from RDSdata.
weight: str, optional. Name of the weight variable. User specified weight variable for a weighted analysis. When set to None, the function performs an unweighted analysis. Default is None.
var_est: str, optional. One of the bootstrap methods or the delta (naive) method. By default the function calculates naive standard errors. Variance estimation options include ‘naive’ or bootstrap methods: ‘chain’, ‘tree_uni’, ‘tree_bi’. Default is None (naive).
resample_n: int, optional. Specifies the number of resample iterations. Note that this argument is None when var_est = ‘naive’. Required for bootstrap methods, default 300.
n_cores: int, optional. Number of CPU cores to use for parallel bootstrap processing. If specified, uses optimized parallel bootstrap. If None, uses standard sequential bootstrap. Default is None.
na_rm: bool, optional. If True (default), observations with missing values in x (or in the weight column, when supplied) are removed before estimation. If False, missing values are retained and the estimator returns NaN whenever NAs are present, mirroring R’s svymean(..., na.rm = FALSE) behaviour. Default is True.
return_bootstrap_means: bool, optional. If True, return the per-iteration estimates along with the main results (only for bootstrap methods). For continuous variables this is a list of scalar means; for categorical variables it is a list of proportion arrays aligned with the level order. Default is False.
return_node_counts: bool, optional. If True, return sample size per iteration along with main results (only for bootstrap methods). Default is False.

Returns

RDSResult or tuple

An RDSResult object containing the following elements:

results: DataFrame; A tidy results table. For continuous variables, columns are Mean and SE with a single row. For categorical variables, columns are Category, Mean, and SE with one row per level. For categorical variables, the reported “Mean” for each level is the estimated proportion of observations in that level.
additional_info: Information about the estimation: (1) SE method: variance estimation method (2) Weight: indicator of whether weighted analysis was used (3) n_Data: total number of observations in the input data (4) n_Analysis: number of observations used in the analysis (after NA removal when na_rm=True) (5) n_Iteration: number of resampling iterations (if SE method is not ‘naive’) (6) n_Dropped: number of bootstrap iterations skipped due to errors (if SE method is not ‘naive’)
resample_summary: Descriptive summary of resamples if var_est is not ‘naive’: mean, SD, min, quartiles, and max of resample sizes
resample_estimates: Per-iteration estimates if var_est is not ‘naive’. For continuous variables, a list of scalar means (one per iteration). For categorical variables, a list of proportion arrays (one per iteration, aligned with the level order).
When return_bootstrap_means=False and return_node_counts=False (default):: Returns RDSResult object only
When return_bootstrap_means=True and return_node_counts=False:: Returns (RDSResult, bootstrap_estimates_list)
When return_bootstrap_means=False and return_node_counts=True:: Returns (RDSResult, node_counts_list)
When return_bootstrap_means=True and return_node_counts=True:: Returns (RDSResult, bootstrap_estimates_list, node_counts_list)

Notes

The RDSResult object is a pandas DataFrame subclass that:

Retains all DataFrame functionality for analysis
Has custom print formatting for clean display
Exposes the tidy results table via result.results and the underlying bootstrap estimates and node counts as attributes

For categorical variables, the reported “Mean” for each level is the estimated proportion of observations in that level. Each level has its own standard error

Integer-coded categorical variables (such as Race=1,2,3) are treated as numeric by default and will produce a single mean rather than per-category proportions. To obtain per-category output, convert the column with data[col] = data[col].astype('category') before calling RDSmean.

Examples

from RDSTools import RDSmean

# Basic mean with naive variance estimation (continuous variable)
result = RDSmean(x='Age', data=rds_data, var_est='naive')

# Weighted analysis with inverse weights
result = RDSmean(x='Age', data=rds_data, weight='WEIGHT')

# Categorical variable: convert to category dtype first
rds_data['Race'] = rds_data['Race'].astype('category')
result = RDSmean(x='Race', data=rds_data, weight='WEIGHT')
# Output is a tidy table with one row per Race level

# Retain NAs and propagate to NaN (instead of dropping)
result = RDSmean(x='Age', data=rds_data, na_rm=False)

# Bootstrap method with resampling
result = RDSmean(
    x='Age',
    data=rds_data,
    weight='WEIGHT',
    var_est='chain',
    resample_n=1000
)

# Categorical bootstrap: per-category proportions and bootstrap SEs
rds_data['Race'] = rds_data['Race'].astype('category')
result = RDSmean(
    x='Race',
    data=rds_data,
    weight='WEIGHT',
    var_est='chain',
    resample_n=300
)

# Parallel processing with 4 cores
result = RDSmean(
    x='Age',
    data=rds_data,
    var_est='tree_uni',
    resample_n=1000,
    n_cores=4
)

# Return bootstrap estimates and node counts
result, bootstrap_estimates, node_counts = RDSmean(
    x='Age',
    data=rds_data,
    var_est='tree_uni',
    resample_n=1000,
    return_bootstrap_means=True,
    return_node_counts=True
)

RDStable - Contingency Tables

Estimating one and two-way tables with respondent driven sampling sample data. One-way tables are constructed by specifying a categorical variable for x argument only. Two-way tables are constructed by specifying two categorical variables for x and y arguments. Standard errors of proportions are calculated using naive or resampling approaches from ‘RDSboot’.

Usage

RDStable(x, y=None, data=None, weight=None, var_est=None, resample_n=None, margins=3, n_cores=None, return_bootstrap_tables=False, return_node_counts=False)

Arguments

x: str. Column name; For a 1-way table, specify one categorical variable. By default the function returns a 1-way table.
y: str, optional. Column name; Optional, for 2-way tables specify the second categorical variable of interest. Default is None.
data: pandas.DataFrame. The output DataFrame from RDSdata.
weight: str, optional. Name of the weight variable. User specified weight variable for a weighted analysis. When set to NULL, the function performs an unweighted analysis. Default is None.
var_est: str, optional. One of the bootstrap methods or the delta (naive) method. By default the function calculates naive standard errors. Variance estimation options include ‘naive’ or bootstrap methods: ‘chain’, ‘tree_uni’, ‘tree_bi’. Default is None (naive).
resample_n: int, optional. Specifies the number of resample iterations. Note that this argument is None when var_est = ‘naive’. Required for bootstrap methods, default 300.
margins: int, optional. For two-way tables: 1=row proportions, 2=column proportions, 3=cell proportions (default). Default is 3.
n_cores: int, optional. Number of CPU cores to use for parallel bootstrap processing. If specified, uses optimized parallel bootstrap. If None, uses standard sequential bootstrap. Default is None.
return_bootstrap_tables: bool, optional. If True, return bootstrap table estimates along with main results (only for bootstrap methods). Default is False.
return_node_counts: bool, optional. If True, return sample size per iteration along with main results (only for bootstrap methods). Default is False.

Returns

RDSTableResult or tuple

An RDSTableResult object containing the following elements:

formula: Formula; Variable(s) used for the estimation
results: DataFrame or tables; Weighted or unweighted proportions (prop_table) and their standard errors (se_table)
additional_info: Information about the estimation: (1) SE method: variance estimation method (2) Weight: indicator of whether weighted analysis was used (3) n_Data: total number of observations in the input data (4) n_Analysis: number of observations used in the analysis (after NA removal on the table variable(s)) (5) n_Iteration: number of resampling iterations (if SE method is not ‘naive’) (6) n_Dropped: number of bootstrap iterations skipped due to errors (if SE method is not ‘naive’)
resample_summary: Descriptive summary of resamples if var_est is not ‘naive’: mean, SD, min, quartiles, and max of resample sizes
resample_estimates: Proportions calculated for each resampling iteration if var_est is not ‘naive’
When return_bootstrap_tables=False and return_node_counts=False (default):: Returns RDSTableResult object only
When return_bootstrap_tables=True and return_node_counts=False:: Returns (RDSTableResult, bootstrap_tables_list)
When return_bootstrap_tables=False and return_node_counts=True:: Returns (RDSTableResult, node_counts_list)
When return_bootstrap_tables=True and return_node_counts=True:: Returns (RDSTableResult, bootstrap_tables_list, node_counts_list)

Notes

The RDSTableResult object is a custom class that:

Provides formatted display of contingency tables
Includes cell counts, proportions, and standard errors
Supports different margin calculations (row, column, cell)
Provides access to bootstrap tables and node counts

Counts vs. proportions under weighting. The reported counts (the n column of a one-way table and the cell counts of a two-way table) are always the unweighted observed counts and do not change when a weight is supplied. The proportions do: with weight=None they are unweighted (count divided by the relevant total), and with a weight column they are weighted (built from the summed weights, following margins for two-way tables). Consequently the % column of a weighted table is not simply n divided by the total.

Standard errors. For the naive (delta) method, unweighted SEs use \(\sqrt{p(1-p)/(n-1)}\), where \(n\) is the number of observations with non-missing table variable(s); for a two-way table this global \(n-1\) is used for every margin. Weighted naive SEs use the supplied weights evaluated against the weighted proportion. For the bootstrap methods, the SE of each cell is the sample standard deviation (ddof=1) of that cell’s proportion across the retained resamples.

Examples

from RDSTools import RDStable

# One-way table
result = RDStable(x="Sex", data=rds_data)

# Two-way table with bootstrap variance estimation
result = RDStable(
    x="Sex",
    y="Race",
    data=rds_data,
    var_est='chain',
    resample_n=100
)

# Two-way table with row proportions and parallel processing
result = RDStable(
    x="Sex",
    y="Race",
    data=rds_data,
    var_est='tree_uni',
    resample_n=1000,
    margins=1,  # row proportions
    n_cores=4
)

# Return bootstrap tables and node counts
result, bootstrap_tables, node_counts = RDStable(
    x="Sex",
    data=rds_data,
    var_est='tree_uni',
    resample_n=1000,
    return_bootstrap_tables=True,
    return_node_counts=True
)

RDSlm - Linear Regression

Linear Regression Modeling with Respondent Driven Sampling (RDS) Sample Data. This function mimics the lm function in R stats package with capabilities to handle RDS data in model estimation. Standard errors of regression coefficients are calculated using naive or resampling approaches from ‘RDSboot’. The dependent variable must be numeric; for a binary outcome use RDSglm.

Usage

RDSlm(data, formula, weight=None, var_est=None, resample_n=None, n_cores=None, return_bootstrap_estimates=False, return_node_counts=False, res_boot=False)

Arguments

data

pandas.DataFrame. The output DataFrame from RDSdata.

formula

str. Description of the model with dependent and independent variables. (e.g., “y ~ x1 + x2”). The dependent variable must be numeric (continuous). If a binary/character/factor response is supplied, RDSlm raises an error directing you to RDSglm.

weight

str, optional. Name of the weight variable. User specified weight variable for a weighted analysis. When set to NULL, the function performs an unweighted analysis. Default is None.

var_est

str, optional. One of the bootstrap methods or the delta (naive) method. By default, the function calculates naive standard errors. Variance estimation options include ‘naive’ or bootstrap methods: ‘chain’, ‘tree_uni’, ‘tree_bi’. Default is None (naive).

resample_n

int, optional. Specifies the number of resample iterations. Note that this argument is None when var_est = ‘naive’. Required for bootstrap methods, default 300.

n_cores

int, optional. Number of CPU cores to use for parallel bootstrap processing. If specified, uses optimized parallel bootstrap. If None, uses standard sequential bootstrap. Default is None.

return_bootstrap_estimates

bool, optional. If True, return bootstrap coefficient estimates along with main results (only for bootstrap methods). Default is False.

return_node_counts

bool, optional. If True, return sample size per iteration along with main results (only for bootstrap methods). Default is False.

res_boot

bool, optional. If True, use a residual bootstrap instead of the default case (network) bootstrap (Davison & Hinkley, 1997). Only valid with a bootstrap var_est method; raises a ValueError otherwise. Both options report the same coefficients – those of the original fit – and differ only in the standard errors. Default is False.

The case bootstrap redraws respondents from the recruitment network and refits on their observed outcomes. The residual bootstrap first restricts to rows that are complete on every term in the formula, draws from those, and rebuilds each drawn row’s outcome from the original fit before refitting. Because each row keeps its own residual, the rebuilt outcome equals the observed one, so the two options differ through which rows are eligible rather than through the outcome values. On data with appreciable missingness in the model variables the resulting standard errors can differ noticeably.

The residual bootstrap is useful when a categorical predictor has enough missing cases that some of its levels fail to appear in a case resample.

Returns

RDSRegressionResult or tuple

An RDSRegressionResult object. print(result) renders the full summary; the values behind it are available as the attributes below.

Note

This object is not a dictionary or a named list. There are no .model_fit, .additional_info, .resample_summary or .resample_estimates attributes – those name sections of the printed output, which are backed by the attributes listed here.

Model and coefficients

formulastr: The model formula used for the estimation.
coefficientspandas.DataFrame: Point estimates, standard errors, t-values and p-values, in columns Estimate, Std.Error, t_values, p_values.
results_object: The fitted statsmodels object for the point estimates. None when var_est is ‘naive’.

Model fit (the “model_fit” section of the printed output)

r_squaredlist of float: [R-squared, adjusted R-squared].
f_statisticlist of float: [F, df_model, df_resid].
residual_std_errorfloat: Residual standard error. Always None for logistic fits.
df_residfloat: Residual degrees of freedom; also the df used for the bootstrap p-values.
logistic_info: Always None for RDSlm; populated only by RDSglm.

Under a resampling var_est these are averages over the retained resamples – see Reporting resampled results below.

Estimation settings (the “additional_info” section of the printed output)

var_est_methodstr: Variance estimation method (‘Naive’ when var_est is None).
is_weightedbool: Whether a weighted analysis was used.
n_original, n_analysisint: Rows in the input data (printed as n_Data), and rows actually used after NA removal across all formula terms (printed as n_Analysis).
n_iterationsint or None: Number of resampling iterations REQUESTED (i.e. resample_n). None when var_est is ‘naive’.
residual_bootstrapbool: Whether the residual bootstrap was used instead of the case bootstrap.

Resampling (the “resample_summary” section of the printed output)

bootstrap_estimateslist of pandas.Series: Coefficients from each RETAINED resample. Empty when var_est is ‘naive’. Also returned separately when return_bootstrap_estimates=True.
node_countslist of int: Size of each retained resample. Empty when var_est is ‘naive’. Also returned separately when return_node_counts=True.
mean_nodes, min_nodes, q1_nodes, median_nodes, q3_nodes, max_nodes: Summary of node_counts. All None when var_est is ‘naive’.

Note

There is no n_Dropped attribute. The printed value is derived as n_iterations - len(node_counts) – the number of requested resamples that were discarded. See Reporting resampled results below.

With return_bootstrap_estimates and/or return_node_counts set, a tuple is returned instead: the result, then the bootstrap estimates, then the node counts, including only the ones requested.

Notes

The three resampling methods each keep the number of seeds in a given resample consistent with the number of seeds in the original sample (\(s\)).

‘chain’ selects \(s\) seeds using SRSWR from all seeds in the original sample and then all nodes in the chains created by each of the resampled seeds are retained.

In the ‘tree_uni’ method, \(s\) seeds are selected using Simple Random Sampling with Replacement (SRSWR) from all seeds. For each selected seed, this method (A) checks its recruit counts, (B) selects SRSWR of the recruits counts from all recruits identified in (A), and (C) for each sampled recruit, this method repeats Steps A and B. (D) Steps A, B, and C continue until reaching the last wave of each chain.

‘tree_bi’ selects \(s\) nodes from the recruitment chains using SRSWR. For each selected node, it (A) checks its connected nodes (i.e., both recruiters and recruits) and their count, (B) from all connected nodes identified in (A), performs SRSWR of the same node count, and (C) for each selected node, performs steps A and B, but does not resample already resampled nodes. (D) Steps A, B, and C are repeated until the end of the chain.

Reporting resampled results

Two things to know when var_est is a resampling method.

Model fit statistics are averages. R-squared, adjusted R-squared, the F-statistic, the residual standard error and the residual degrees of freedom are means over the resamples that were retained, not the fit statistics of your model. The coefficients themselves are always taken from the original fit, never averaged.

Resamples can be dropped. A resample that fails to fit, or that is degenerate and so carries no information, is discarded. Dropped resamples are excluded from the standard errors, from the averaged fit statistics, and from the resample summary. The count is reported as n_Dropped in the output, and a single warning summarises how many were dropped and why. A high proportion usually indicates a sparse factor level or very small resamples; collapsing sparse levels is the usual remedy.

Examples

from RDSTools import RDSlm

# Linear regression (continuous dependent variable)
result = RDSlm(
    data=rds_data,
    formula="Outcome_cont ~ Age + C(Sex)",
    weight='WEIGHT',
    var_est='chain',
    resample_n=1000
)

# Parallel regression with multiple predictors
result = RDSlm(
    data=rds_data,
    formula="Outcome_cont ~ Age + C(Sex) + C(Race)",
    var_est='tree_uni',
    resample_n=1000,
    n_cores=4
)

# Return bootstrap estimates and node counts
result, bootstrap_estimates, node_counts = RDSlm(
    data=rds_data,
    formula="Outcome_cont ~ Age + C(Sex)",
    var_est='tree_uni',
    resample_n=1000,
    return_bootstrap_estimates=True,
    return_node_counts=True
)

RDSglm - Logistic Regression

Logistic Regression Modeling with Respondent Driven Sampling (RDS) Sample Data. This function mimics the glm function (family = binomial) in R stats package with capabilities to handle RDS data in model estimation. Standard errors of regression coefficients are calculated using naive or resampling approaches from ‘RDSboot’. The dependent variable must be binary; for a numeric (continuous) outcome use RDSlm.

Usage

RDSglm(data, formula, weight=None, var_est=None, resample_n=None, n_cores=None, return_bootstrap_estimates=False, return_node_counts=False, res_boot=False)

Arguments

data

pandas.DataFrame. The output DataFrame from RDSdata.

formula

str. Description of the model with dependent and independent variables. (e.g., “y ~ x1 + x2”). The dependent variable must be binary (character, factor, or a variable with exactly two distinct non-null levels). If a numeric/continuous response is supplied, RDSglm raises an error directing you to RDSlm.

weight

str, optional. Name of the weight variable. User specified weight variable for a weighted analysis. When set to NULL, the function performs an unweighted analysis. Default is None.

var_est

str, optional. One of the bootstrap methods or the delta (naive) method. By default, the function calculates naive standard errors. Variance estimation options include ‘naive’ or bootstrap methods: ‘chain’, ‘tree_uni’, ‘tree_bi’. Default is None (naive).

resample_n

int, optional. Specifies the number of resample iterations. Note that this argument is None when var_est = ‘naive’. Required for bootstrap methods, default 300.

n_cores

int, optional. Number of CPU cores to use for parallel bootstrap processing. If specified, uses optimized parallel bootstrap. If None, uses standard sequential bootstrap. Default is None.

return_bootstrap_estimates

bool, optional. If True, return bootstrap coefficient estimates along with main results (only for bootstrap methods). Default is False.

return_node_counts

bool, optional. If True, return sample size per iteration along with main results (only for bootstrap methods). Default is False.

res_boot

bool, optional. If True, use a residual bootstrap instead of the default case (network) bootstrap (Davison & Hinkley, 1997). Only valid with a bootstrap var_est method; raises a ValueError otherwise. Both options report the same coefficients – those of the original fit – and differ only in the standard errors. Default is False.

Because the outcome is binary there are no residuals to reuse, so this option regenerates it. For each resample the fitted probability of every drawn respondent is computed from the original coefficients, their outcome is redrawn from that probability, and the model is refit. This makes it a parametric bootstrap in the sense of Davison & Hinkley (1997, ch. 7).

Two consequences are worth noting before choosing it. It assumes the fitted model is correct, so it measures variability under that assumption and cannot detect a misspecified model; its standard errors are typically smaller than the case bootstrap’s, and the two can disagree on whether a borderline coefficient is significant. State which option you used when reporting results. It is also far less prone to separation, since a redrawn outcome rarely produces the degenerate configurations that redrawing real respondents does.

The residual bootstrap is useful when a categorical predictor has enough missing cases that some of its levels fail to appear in a case resample.

Outcome coding

A two-level response is recoded to an explicit 0/1 column before fitting, using a single predictable convention: the alphabetically-first level becomes 0 (baseline / reference) and the second becomes 1 (success). The model therefore estimates the log-odds of the success level relative to the baseline, and the output states the direction explicitly (e.g., Coefficients: log-odds of M vs. reference F). A response already supplied as numeric 0/1 is left as coded (success = 1, baseline = 0).

Returns

RDSRegressionResult or tuple

An RDSRegressionResult object. print(result) renders the full summary; the values behind it are available as the attributes below.

Note

This object is not a dictionary or a named list. There are no .model_fit, .additional_info, .resample_summary or .resample_estimates attributes – those name sections of the printed output, which are backed by the attributes listed here.

Model and coefficients

formulastr: The model formula used for the estimation.
coefficientspandas.DataFrame: Point estimates, standard errors, z-values and p-values on the log-odds scale, in columns Estimate, Std.Error, z value, p_values. Note the column is z value (with a space), not t_values as in RDSlm.
results_object: The fitted statsmodels GLM object for the point estimates. None when var_est is ‘naive’.

Model fit (the “model_fit” section of the printed output)

logistic_infodict: Keys null_deviance, residual_deviance, df_null, df_resid, aic, plus success_label and baseline_label recording which outcome level is the modelled event (see Outcome coding above).
df_residfloat: Residual degrees of freedom. Not used for the p-values, which are computed on the normal scale.
residual_std_error: Always None for logistic fits.
r_squared, f_statistic: Placeholders (NaN); not defined for logistic regression.

Under a resampling var_est the deviances, AIC and df_resid are averages over the retained resamples – see Reporting resampled results below. df_null comes from the original fit.

Estimation settings (the “additional_info” section of the printed output)

var_est_methodstr: Variance estimation method (‘Naive’ when var_est is None).
is_weightedbool: Whether a weighted analysis was used.
n_original, n_analysisint: Rows in the input data (printed as n_Data), and rows actually used after NA removal across all formula terms (printed as n_Analysis).
n_iterationsint or None: Number of resampling iterations REQUESTED (i.e. resample_n). None when var_est is ‘naive’.
residual_bootstrapbool: Whether the residual bootstrap was used instead of the case bootstrap.

Resampling (the “resample_summary” section of the printed output)

bootstrap_estimateslist of pandas.Series: Coefficients from each RETAINED resample. Empty when var_est is ‘naive’. Also returned separately when return_bootstrap_estimates=True.
node_countslist of int: Size of each retained resample. Empty when var_est is ‘naive’. Also returned separately when return_node_counts=True.
mean_nodes, min_nodes, q1_nodes, median_nodes, q3_nodes, max_nodes: Summary of node_counts. All None when var_est is ‘naive’.

Note

There is no n_Dropped attribute. The printed value is derived as n_iterations - len(node_counts) – the number of requested resamples that were discarded. See Reporting resampled results below.

With return_bootstrap_estimates and/or return_node_counts set, a tuple is returned instead: the result, then the bootstrap estimates, then the node counts, including only the ones requested.

Notes

The three resampling methods each keep the number of seeds in a given resample consistent with the number of seeds in the original sample (\(s\)).

‘chain’ selects \(s\) seeds using SRSWR from all seeds in the original sample and then all nodes in the chains created by each of the resampled seeds are retained.

In the ‘tree_uni’ method, \(s\) seeds are selected using Simple Random Sampling with Replacement (SRSWR) from all seeds. For each selected seed, this method (A) checks its recruit counts, (B) selects SRSWR of the recruits counts from all recruits identified in (A), and (C) for each sampled recruit, this method repeats Steps A and B. (D) Steps A, B, and C continue until reaching the last wave of each chain.

‘tree_bi’ selects \(s\) nodes from the recruitment chains using SRSWR. For each selected node, it (A) checks its connected nodes (i.e., both recruiters and recruits) and their count, (B) from all connected nodes identified in (A), performs SRSWR of the same node count, and (C) for each selected node, performs steps A and B, but does not resample already resampled nodes. (D) Steps A, B, and C are repeated until the end of the chain.

Reporting resampled results

Two things to know when var_est is a resampling method.

Model fit statistics are averages. The null and residual deviances, the AIC and the residual degrees of freedom are means over the resamples that were retained, not the fit statistics of your model. The coefficients themselves are always taken from the original fit, never averaged.

Resamples can be dropped. A resample that fails to fit, or that is degenerate and so carries no information, is discarded. Dropped resamples are excluded from the standard errors, from the averaged fit statistics, and from the resample summary. The count is reported as n_Dropped in the output, and a single warning summarises how many were dropped and why. A high proportion usually indicates a sparse factor level or very small resamples; collapsing sparse levels is the usual remedy.

Examples

from RDSTools import RDSglm

# Logistic regression (binary dependent variable)
result = RDSglm(
    data=rds_data,
    formula="Outcome_cat ~ Age + C(Sex)",
    weight='WEIGHT',
    var_est='chain',
    resample_n=100
)

References

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press.

Handcock, M. S., Fellows, I. E., & Gile, K. J. (2024). RDS: Respondent-Driven Sampling (R package version 0.9-9). https://CRAN.R-project.org/package=RDS

Salganik, M. J. (2006). Variance estimation, design effects, and sample size calculations for respondent-driven sampling. Journal of Urban Health, 83(1), i98-i112.

Volz, E., & Heckathorn, D. D. (2008). Probability based estimation theory for respondent driven sampling. Journal of Official Statistics, 24(1), 79-97.