Package {paneltests}

Type:	Package
Title:	Panel Data Pre-Testing and Diagnostic Suite
Version:	1.0.8
Date:	2026-10-30
Description:	Pre-testing and diagnostic tools for panel data analysis. Researchers should run these tests before any panel regression to verify modelling assumptions. The package implements: (1) the Hsiao (2014, <ISBN:978-1-107-65763-2>) homogeneity F-tests (F1/F2/F3), Swamy (1970) <doi:10.2307/1913012> parameter heterogeneity test, and Pesaran (2004) <doi:10.2139/ssrn.572504> cross-sectional dependence test via xtpretest(); (2) missing-data detection, mechanism testing, and imputation for unbalanced panels via xtmispanel(); (3) quantile-regression cross-sectional dependence tests (T_tau and T-tilde_tau statistics) of Demetrescu, Hosseinkouchack and Rodrigues (2023) via xtcsdq(); and (4) the panel quantile-regression slope homogeneity S-hat and D-hat statistics of Galvao, Juhl, Montes-Rojas and Olmo (2017) <doi:10.1093/jjfinec/nbx016> via xtqsh(). Together these tests address three fundamental pre-testing questions: (i) are slopes homogeneous? (ii) is there cross-sectional dependence? and (iii) is the panel balanced and is missingness ignorable?
License:	GPL-3
Encoding:	UTF-8
Depends:	R (≥ 3.5.0)
Imports:	stats, utils
Suggests:	testthat (≥ 3.0.0), plm, zoo, quantreg
Config/testthat/edition:	3
NeedsCompilation:	no
RoxygenNote:	7.3.1
Packaged:	2026-10-31 05:38:52 UTC; root
Author:	Muhammad Abdullah Alkhalaf [aut, cre, cph]
Maintainer:	Muhammad Abdullah Alkhalaf <muhammedalkhalaf@gmail.com>
Repository:	CRAN
Date/Publication:	2026-10-31 06:50:08 UTC

Print method for xtcsdq objects

Description

Print method for xtcsdq objects

Usage

## S3 method for class 'xtcsdq'
print(x, ...)

Arguments

Value

Invisibly returns x.

Print Method for xtqsh Objects

Description

Prints a formatted summary of an "xtqsh" test result.

Usage

## S3 method for class 'xtqsh'
print(x, ...)

Arguments

Value

Invisibly returns x.

Sample Panel Dataset for Quantile Slope Homogeneity Testing

Description

A simulated balanced panel dataset for demonstrating the quantile slope homogeneity test (xtqsh).

Usage

data(qsh_sample)

Format

A data frame with columns:

id

Cross-sectional unit identifier.

time

Time period identifier.

y

Dependent variable.

x1

First explanatory variable.

x2

Second explanatory variable.

Summary method for xtcsdq objects

Description

Summary method for xtcsdq objects

Usage

## S3 method for class 'xtcsdq'
summary(object, ...)

Arguments

Value

Invisibly returns object.

Summary Method for xtqsh Objects

Description

Prints a summary of an "xtqsh" test result.

Usage

## S3 method for class 'xtqsh'
summary(object, ...)

Arguments

Value

Invisibly returns object.

Tests of No Cross-Sectional Dependence in Panel Quantile Regressions

Description

Tests the null hypothesis of no cross-sectional error dependence (CSD) in panel quantile regressions. Implements the T_tau and T-tilde_tau statistics of Demetrescu, Hosseinkouchack and Rodrigues (2023).

Usage

xtcsdq(
  formula = NULL,
  data = NULL,
  index = NULL,
  quantiles,
  mode = c("pooled", "individual", "residuals"),
  residuals = NULL,
  bandwidth = NULL,
  correction = TRUE
)

Arguments

Details

The T_tau statistic (Equation 3 in Demetrescu et al., 2023) tests for CSD by examining pairwise correlations of demeaned QR residuals across units. Under the null of no CSD, T_tau is asymptotically standard normal.

The bias-corrected version T-tilde_tau (Equation 5) subtracts two correction terms that account for the estimation uncertainty in the QR slope and the sparsity at the quantile. Reject H0 for large positive values.

The portmanteau statistic M_K = K^{-1} \sum_{q=1}^K T_\tau^{(q)} aggregates across K quantile levels.

The KDE bandwidth defaults to h = 0.35 (NT)^{-0.2} as in the original paper.

Value

An object of class "xtcsdq" with components:

T_tau

Numeric vector of T_tau statistics (one per quantile).

Ttilde_tau

Numeric vector of bias-corrected T-tilde_tau statistics.

pval_T

p-values for T_tau.

pval_Ttilde

p-values for T-tilde_tau.

fhat

KDE density estimates at zero (one per quantile).

M_K

Portmanteau statistic (average of T_tau over quantiles).

Mtilde_K

Bias-corrected portmanteau statistic.

pval_M

p-value for M_K.

pval_Mc

p-value for Mtilde_K.

quantiles

Quantile levels used.

N

Number of cross-sectional units.

TT

Number of time periods.

bandwidth

KDE bandwidth used.

References

Demetrescu, M., Hosseinkouchack, M. and Rodrigues, P.M.M. (2023). Tests of no cross-sectional error dependence in panel quantile regressions. Ruhr Economic Papers, No. 1041. doi:10.4419/96973210

Examples

set.seed(42)
n <- 8; tt <- 20
dat <- data.frame(
  id   = rep(1:n, each = tt),
  time = rep(1:tt, times = n),
  y    = rnorm(n * tt),
  x1   = rnorm(n * tt)
)
res <- xtcsdq(y ~ x1, data = dat, index = c("id", "time"),
              quantiles = c(0.25, 0.5, 0.75))
print(res)
summary(res)

Kao (1999) Panel Cointegration Tests

Description

Residual-based panel cointegration tests of Kao (1999) with a common cointegrating vector and panel fixed effects: the modified DF t, DF t and ADF t (which allow endogenous regressors through the long-run variance adjustment) and the unadjusted modified DF t and DF t (strict exogeneity, no serial correlation). The statistics are those of Kao (1999); the sample conventions are those of the Stata command xtcointtest kao, which four of the five statistics reproduce numerically (see Details). The p-values are left-tail normal probabilities, the direction of rejection stated by Kao (1999).

Usage

xtkao(
  data,
  formula,
  index,
  lags = 1L,
  lag_select = c("none", "aic", "bic"),
  kernel_lags = NULL
)

Arguments

Details

Following Stata, the sample first loses one period to the AR(1) regressions of each variable on its own lag (pooled, without constant) whose residuals w_{it} = (u_{it}, \epsilon_{it}')' enter the long-run covariance matrices. The matrices are computed per panel on the within-panel demeaned residuals with a Bartlett kernel, averaged over panels, and the conditional variances \hat\sigma_\nu^2 = \hat\sigma_u^2 - \hat\Sigma_{u\epsilon} \hat\Sigma_{\epsilon\epsilon}^{-1} \hat\Sigma_{\epsilon u} and \hat\omega_\nu^2 (same with the long-run matrix) are taken from the averaged matrices. The fixed-effects regression of y on x is estimated on the remaining T_0 - 1 periods, and the pooled DF regression \hat e_{it} = \rho \hat e_{i,t-1} + \nu_{it} (no constant) on T = T_0 - 2 periods per panel gives \hat\rho and t_\rho = (\hat\rho - 1)/se, with the residual variance s_e^2 = (NT)^{-1}\sum\sum \hat\nu_{it}^2 (Kao 1999, p. 7). The ADF regression (Kao 1999, eq. 9) adds p lagged differences and is estimated on the T - p periods per panel for which the lags exist; its t statistic is t_{ADF} = (\hat\rho - 1)[\sum_i \hat e_i' Q_i \hat e_i]^{1/2} / s_\nu with s_\nu^2 = (NT)^{-1}\sum_i\sum_t \hat\nu_{itp}^2 (Kao 1999, p. 9-10), where T is the number of periods of the DF step reported as T (not the number of ADF observations N(T - p)). Versions up to 1.0.7 divided by the number of ADF observations.

All five statistics are standard normal under the null and diverge to minus infinity under the alternative (Kao 1999, Theorem 2, Corollary 2 and Remarks 6 and 8), so the p-values are \Phi(z), z being the standardized statistic. Versions up to 1.0.7 returned 1 - \Phi(|z|), which rejects a true null at twice the nominal rate.

Kao (1999) tabulates finite-sample sizes for one regressor only (Table 4); the function warns when there are more than seven regressors (no finite-sample evidence at all), when N < 2 (the standardization is asymptotic in N) or when the panel has fewer than 10 periods.

Agreement with Stata. The unadjusted statistics reproduce xtcointtest kao to at least 1e-6; the modified DF t and DF t do so when the same kernel bandwidth is used for all panels (verified on a six-country panel, four specifications, bandwidths 0, 1 and 2). Two conventions of that command are kept for this agreement and are the package's choice: the innovations entering the long-run covariance matrices are the residuals of pooled AR(1) regressions, demeaned within panel, rather than the first differences of Kao's eqs. (10)-(12), and the fixed-effects regression uses the T_0 - 1 periods after that step. The ADF t follows the paper's s_\nu^2 = RSS/(NT); Stata's ADF t differs from it by up to 0.19 (standardized units) on the reference data, and its internal convention could not be identified from the documentation (known gap). Stata's default bandwidth is chosen per panel by the Newey and West (1994) algorithm; it is not reproduced here.

Value

An object of class "xtkao": a list with stats, p (one-sided left-tail p-values pnorm(stat)), rho, t_rho, t_adf, adf_lags, kernel_lags, sigma2_nu, omega2_nu, N, T and call.

References

Kao, C. (1999). Spurious regression and residual-based tests for cointegration in panel data. Journal of Econometrics, 90(1), 1-44. doi:10.1016/S0304-4076(98)00023-2

Examples

set.seed(2)
N <- 6; TT <- 20
d <- do.call(rbind, lapply(1:N, function(i) {
  x <- cumsum(rnorm(TT)); y <- i + 0.5 * x + rnorm(TT)
  data.frame(id = i, t = 1:TT, y = y, x = x) }))
xtkao(d, y ~ x, index = c("id", "t"), kernel_lags = 1)

Missing Data Detection and Imputation for Panel Data

Description

Detects, diagnoses, and imputes missing values in panel (longitudinal) data sets. The function can produce summary tables (Module 1), test the missingness mechanism (Module 2), impute a target variable (Module 3), and run a cross-method sensitivity analysis (Module 4).

Usage

xtmispanel(
  data,
  vars = NULL,
  index,
  detect = TRUE,
  test = FALSE,
  impute = NULL,
  target = NULL,
  new_var = NULL,
  sensitivity = FALSE,
  knn_k = 5L
)

Arguments

Value

A list (invisibly) with components:

detect

Summary statistics per variable/panel/period.

test

MCAR and MAR test results.

imputed

The data frame augmented with the imputed column (when imputation is requested).

impute_stats

Summary comparing original vs imputed.

sensitivity

Sensitivity analysis results.

References

Little, R. J. A. (1988). A test of missing completely at random for multivariate data with missing values. Journal of the American Statistical Association, 83(404), 1198-1202. doi:10.1080/01621459.1988.10478722

Examples

set.seed(1)
df <- data.frame(
  id   = rep(1:4, each = 8),
  time = rep(1:8, times = 4),
  y    = c(rnorm(32))
)
# introduce some NAs
df$y[c(3, 11, 20)] <- NA
res <- xtmispanel(df, vars = "y", index = c("id", "time"), detect = TRUE)

Pedroni (1999, 2004) Panel Cointegration Tests

Description

Residual-based panel cointegration tests of Pedroni (1999, 2004) with panel-specific cointegrating vectors: four "panel" (same-AR) statistics (modified variance ratio, modified Phillips-Perron t, Phillips-Perron t, ADF t) and three "group" (panel-specific-AR) statistics (modified Phillips-Perron t, Phillips-Perron t, ADF t). The statistics are those of Pedroni (1999, Table 1); the sample conventions are those of the Stata command xtcointtest pedroni, which the statistics reproduce numerically (see Details). The p-values follow the tails stated by Pedroni (1999, p. 668).

Usage

xtpedroni(
  data,
  formula,
  index,
  trend = FALSE,
  lags = 1L,
  lag_select = c("none", "aic", "bic"),
  kernel_lags = NULL
)

Arguments

Details

Let \hat e_{it} be the residuals of the panel-specific level regression on all T_0 periods. All sums run over the T = T_0 - 1 periods for which first differences exist. For each panel the DF regression \Delta\hat e_{it} = (\rho_i - 1) \hat e_{i,t-1} + u_{it} (no constant) is estimated; its residuals are demeaned and give \hat s_i^2 = \sum u_{it}^2 / T, the Bartlett long-run variance \hat\sigma_i^2 of u_{it} (autocovariances divided by T) and \hat\lambda_i = (\hat\sigma_i^2 - \hat s_i^2)/2. \hat L_{11i}^2 is the conditional long-run variance of \Delta y given \Delta x, computed from the Bartlett long-run covariance matrix of the demeaned first differences. The ADF regression (panel-specific \rho_i, no constant) on the T - p periods with lags = p lagged differences available gives, from its demeaned residuals, \hat s_i^{*2}; the ADF statistics use the sums \sum \hat e_{i,t-1}\Delta\hat e_{it} and \sum \hat e_{i,t-1}^2 over that reduced sample.

Standardization uses (\chi - \mu\sqrt N)/\sqrt\nu. For k = 1 regressor the moments are those of Pedroni (2004, Corollary 1): case 2 (estimated fixed effects) when trend = FALSE and case 3 (estimated fixed effects and trends) when trend = TRUE. For k = 2, \dots, 7 they are those of Pedroni (1999, Table 2) with m = k, rows "heterogeneous intercepts included" and "heterogeneous deterministic trends and intercepts included". More than seven regressors are refused because no moments are tabulated. The moments are large-T approximations; the function warns when N < 2 (the standardization is asymptotic in N) or when the panel has fewer than 10 periods.

Direction of rejection and p-values. The raw statistics are Pedroni's: under the alternative the panel variance ratio diverges to plus infinity and the other six statistics diverge to minus infinity (Pedroni 1999, p. 668). The p-values are therefore 1 - \Phi(z) for the panel variance ratio and \Phi(z) for the other six. Versions up to 1.0.7 returned 1 - \Phi(|z|) for all seven statistics, which rejects a true null at twice the nominal rate and gives a small p-value to a statistic of the wrong sign.

Agreement with Stata. With the same kernel bandwidth and ADF lag, all seven standardized statistics reproduce xtcointtest pedroni to at least 1e-6 (verified on a six-country panel, four specifications with four to six regressors, bandwidths 0, 1 and 2). Two conventions of that command are kept because they are needed for this agreement and are stated here as the package's choice: the residuals of the DF and ADF regressions are demeaned before the variances are computed, and the panel ADF t uses \tilde s^{*2} = N^{-1}\sum_i \hat L_{11i}^{-2}\hat s_i^{*2} (weighted), whereas Pedroni (1999, Table 1) writes the unweighted average. The p-values are not part of the comparison; they follow the paper as described above. Stata's default bandwidth is chosen per panel by the Newey and West (1994) algorithm and the header reports the average; that algorithm is not reproduced here, so the default rule of this function (or an integer kernel_lags) will in general differ from a Stata run with kernel(bartlett nwest) unless all panels received the same bandwidth (as when the reported average is an integer such as 0.00).

Value

An object of class "xtpedroni": a list with stats (standardized statistics), p (one-sided p-values in the tail stated by Pedroni (1999, p. 668): 1 - pnorm(z) for the panel variance ratio, which diverges to plus infinity under the alternative, and pnorm(z) for the other six statistics, which diverge to minus infinity), tail (the tail used for each statistic), raw (the unstandardized statistics), moments (means and variances used), N, T, k, adf_lags, kernel_lags and call.

References

Pedroni, P. (1999). Critical values for cointegration tests in heterogeneous panels with multiple regressors. Oxford Bulletin of Economics and Statistics, 61(S1), 653-670. doi:10.1111/1468-0084.61.s1.14

Pedroni, P. (2004). Panel cointegration: asymptotic and finite sample properties of pooled time series tests with an application to the PPP hypothesis. Econometric Theory, 20(3), 597-625. doi:10.1017/S0266466604203073

Examples

set.seed(1)
N <- 6; TT <- 20
d <- do.call(rbind, lapply(1:N, function(i) {
  x <- cumsum(rnorm(TT)); y <- 1 + 0.5 * x + rnorm(TT)
  data.frame(id = i, t = 1:TT, y = y, x = x) }))
r <- xtpedroni(d, y ~ x, index = c("id", "t"), kernel_lags = 2)
r$stats

Comprehensive Panel Data Pre-Testing Suite

Description

Performs a full battery of panel data pre-tests: Hsiao (2014) homogeneity F-tests, robust (HC1) versions, Swamy (1970) parameter heterogeneity test, cross-sectional dependence (Pesaran 2004), and panel summary statistics.

Usage

xtpretest(data, formula, index, tests = "ALL", level = 0.05)

Arguments

Details

Input checks. Missing values in the response or the regressors are refused with an error that reports their number and row positions; the tests have no defined treatment of missing cells. Fewer than two panels, or any panel with fewer than K + 2 observations (so that the individual regression of Hsiao's S_1 has no residual degrees of freedom), are refused with an error naming the panels. Exactly collinear regressor columns are detected from the rank of the QR decomposition of the pooled design and removed with a warning naming them; K is the rank, so the degrees of freedom refer to the regressors that remain. A regressor that is constant within one panel is not collinear in the pooled design; the HSIAO and HETEROGENEITY modules then stop with a message naming the panel (recorded in failed) because the individual regressions are not estimable, while the ROBUST module drops the aliased interaction columns and reports them.

Hsiao's F tests and their labels. The module HSIAO reports three F statistics labelled F1, F2 and F3 in the order overall homogeneity, slope homogeneity and intercept homogeneity. In Hsiao (2014, section 2.2.2) these are, respectively, eq. (2.2.14) (there called F_3), eq. (2.2.15) (there called F_1) and eq. (2.2.16) (there called F_4). The formulas and degrees of freedom are those of the book; only the labels differ, and they are kept for backward compatibility of the returned list.

Swamy's test. The module HETEROGENEITY computes Swamy (1970, eq. 6.2): H = \sum_i (b_i - \hat\beta)' X_i' X_i (b_i - \hat\beta) / s_{ii}, where b_i are the slopes of the individual OLS regressions, X_i the within-panel demeaned regressors, s_{ii} = RSS_i / (T_i - K - 1), and \hat\beta = [\sum_i X_i'X_i / s_{ii}]^{-1} \sum_i (X_i'X_i / s_{ii}) b_i is the weighted pooled estimator of the paper. Versions up to 1.0.7 centred the statistic on the unweighted fixed-effects estimator, which over-rejects under cross-panel heteroskedasticity. H is referred to a chi-square with K(N - 1) degrees of freedom.

Cross-sectional dependence. The module CSD computes Pesaran's CD statistic \sqrt{2/(N(N-1))} \sum_{i<j} \sqrt{T_{ij}} \hat\rho_{ij} from the residuals of the fixed-effects (within) regression with common slopes, using the pairwise-complete T_{ij} overlapping periods for each pair, with a two-sided normal p-value. The residuals of N individual OLS regressions would give a different value; the fixed-effects residuals are the package's choice.

ROBUST module and its size. The "robust" module is an extension of this package and is not part of Hsiao (2014), who only notes that the F-tests assume i.i.d. errors. It fits the fully interacted regression y = a + Xb + \sum_{i>1} D_i g_i + \sum_{i>1} (D_i X) h_i + u, with the first panel as reference, and computes HC1 Wald statistics (divided by the number of restrictions and referred to an F distribution) for slope homogeneity (h_i = 0, (N-1)K restrictions) and for intercept homogeneity given heterogeneous slopes (g_i = 0, N-1 restrictions). Columns aliased in the interacted regression (for example a regressor that is constant within a panel) are dropped and reported. A failure in any module no longer aborts the other modules.

The HC1 Wald statistic has (N - 1)K restrictions and (K + 1)N parameters, and it over-rejects a true null at small T. In the simulations of the 1.0.8 validation (i.i.d. normal errors, heterogeneous intercepts, homogeneous slopes, K = 2, nominal 5 percent) the rejection rates of the robust slope test were 33.4 percent (N = 10, T = 20; 8000 replications, Monte Carlo standard error 0.5 percentage points), 64.8 percent (N = 25, T = 20), 15.4 percent (N = 10, T = 50) and 11.8 percent (N = 25, T = 100); the last three come from 500 replications (standard error about 2 percentage points). The classical F test in the same cells rejects at 3.4 to 6.4 percent. The printed output repeats this note. Use the classical F test (with caution under heteroskedasticity, where it reached 8.4 percent) or a bootstrap of the Wald statistic; the estimator itself is unchanged.

Value

A list (invisibly) with components:

summary

Panel summary statistics.

hsiao

Hsiao homogeneity F-test results.

robust

Robust HC1 Wald versions of the Hsiao F2 and F3 tests (see Details), with the names of any collinear columns dropped.

swamy

Swamy heterogeneity test results.

csd

Cross-sectional dependence test results.

recommendation

Character. Suggested estimator.

failed

Named list of error messages for modules that failed and were skipped (absent when all modules ran).

dropped

Character vector of regressor columns removed because they were exactly collinear with the others (absent when none).

References

Hsiao, C. (2014). Analysis of Panel Data (3rd ed.). Cambridge University Press. doi:10.1017/CBO9781139839327

Swamy, P. A. V. B. (1970). Efficient inference in a random coefficient regression model. Econometrica, 38(2), 311-323. doi:10.2307/1913012

Pesaran, M. H. (2004). General diagnostic tests for cross section dependence in panels. Cambridge Working Paper in Economics, No. 0435. doi:10.2139/ssrn.572504

Examples

set.seed(10)
n <- 5; t <- 10
df <- data.frame(
  id   = rep(1:n, each = t),
  time = rep(1:t, times = n),
  y    = rnorm(n * t),
  x1   = rnorm(n * t)
)
res <- xtpretest(df, y ~ x1, index = c("id", "time"),
                 tests = c("hsiao", "csd"))

Quantile Regression Slope Homogeneity Test for Panel Data

Description

Tests the null hypothesis of slope homogeneity in panel quantile regressions. Implements the S-hat and D-hat statistics of Galvao et al. (2017).

Usage

xtqsh(formula, data, index, tau, bw = "hallsheather", marginal = FALSE)

Arguments

Value

An object of class "xtqsh" containing test statistics and p-values.

References

Galvao, A.F., Juhl, T., Montes-Rojas, G. and Olmo, J. (2017). Testing Slope Homogeneity in Quantile Regression Panel Data. Journal of Financial Econometrics, 16(2), 211-243.

Examples

set.seed(42)
n <- 10; tt <- 20
dat <- data.frame(
  id   = rep(1:n, each = tt),
  time = rep(1:tt, times = n),
  y    = rnorm(n * tt),
  x1   = rnorm(n * tt)
)
res <- xtqsh(y ~ x1, data = dat, index = c("id", "time"), tau = 0.5)
print(res)