Fit a Bayesian meta-analysis model across study designs

Fits a hierarchical Bayesian model synthesising treatment effects from studies with different designs: difference-in-differences (DiD), randomised controlled trials (RCT), and pre-post studies. All designs contribute to a shared population treatment effect.

Usage

meta_did(
  summary_data = NULL,
  individual_data = NULL,
  normalise_by_baseline = TRUE,
  robust_heterogeneity = FALSE,
  design_effects = FALSE,
  hierarchical_rho = TRUE,
  correlated_effects = FALSE,
  baseline_imbalance = c("by_randomisation", "estimated", "fixed_zero"),
  mu_gamma = c("zero", "estimated"),
  kappa = 0.5,
  cluster_deff_default = 2,
  covariates = NULL,
  multiplicative_covariate = NULL,
  center_covariates = TRUE,
  priors = set_priors(),
  method = c("sample", "optimize"),
  chains = 4L,
  iter_warmup = 1000L,
  iter_sampling = 1000L,
  seed = NULL,
  allow_no_did = FALSE,
  allow_unidentified_kappa = FALSE,
  ...
)

Arguments

summary_data

A data frame with one row per study containing summary statistics. Must include columns study_id and design. See validate_summary_data() for the full column specification per design. Valid designs: "did", "did_change", "rct", "pp".

individual_data

A data frame in long format with one row per observation. Must include columns study_id, design, group, time, and value. Valid designs: "did", "rct", "pp". No study_id may appear in both summary_data and individual_data.

normalise_by_baseline

Logical. If TRUE (default), all means and SDs are divided by each study's pre-treatment control mean (or the grand mean for change-only studies), placing outcomes on a common fractional scale. The reported treatment_effect_mean is then the population mean of the per-study proportional effects, \(E[\theta_i / b_i]\) (a percentage-scale effect, each study expressed as a fraction of its own baseline), which is the appropriate estimand when studies are on heterogeneous scales. Note this is not \(E[\theta] / E[b]\): when baselines vary across studies the two differ by the between-study baseline coefficient of variation squared (Jensen's inequality).

robust_heterogeneity

Logical. If TRUE, study-level treatment effects are drawn from a Student-t distribution rather than a normal, providing robustness to outlier studies. The degrees-of-freedom parameter is estimated with the prior specified in priors$nu.

design_effects

Logical. If TRUE, additive offsets on the population treatment effect mean are estimated for RCT and Pre-Post studies relative to DiD (the reference). Useful for testing whether designs yield systematically different effect estimates.

hierarchical_rho

Logical. If TRUE (default), the pre-post correlation is modelled hierarchically across studies. Studies with a reported correlation inform the population distribution; studies without one have their correlation imputed.

correlated_effects

Logical. If TRUE, study-level treatment effects and time trends are drawn jointly from a bivariate normal with a shared correlation parameter, rather than independently. The correlation is parameterised via a Cholesky factor of a 2×2 correlation matrix with an LKJ prior (see set_priors()). Cannot be combined with robust_heterogeneity = TRUE. Default FALSE.

baseline_imbalance

How the per-study baseline difference \(\gamma_i\) is modelled. One of:

"by_randomisation"

(Default) Each study's \(\gamma_i\) follows from its randomisation column. Non-randomised studies draw \(\gamma_i \sim N(\mu_\gamma, \tau_\gamma)\); randomised studies draw \(\gamma_i \sim N(0, \kappa^2 s_i^2)\), where \(s_i\) is the sampling SD of that study's baseline contrast. The two populations do not share a mean: randomisation implies a zero population imbalance structurally, so it is imposed rather than estimated.

"estimated"

Every DiD and RCT study draws \(\gamma_i \sim N(\mu_\gamma, \tau_\gamma)\), ignoring the randomisation column entirely. This was the previous default.

"fixed_zero"

Fix \(\gamma_i = 0\) for RCT studies; DiD studies are unaffected and still estimate \(\gamma_i\) from their own pre-treatment means. Note this is a hard constraint, which costs a DiD study its robustness to baseline imbalance: with \(\gamma_i\) pinned at zero the model averages the pre- and post-period information instead of differencing it, so a real imbalance leaks into \(\theta_i\). Prefer "by_randomisation" with a small kappa, which shrinks toward zero without imposing it.

Baseline imbalance is unidentified for post-only studies: it subtracts directly from their estimated effect, so whatever the model assumes about \(\gamma\) propagates straight into the pooled treatment effect for those studies. The default exists to keep that propagation honest.

mu_gamma

Whether the population mean baseline imbalance among non-randomised studies is estimated. One of:

"zero"

(Default) \(\mu_\gamma = 0\). The magnitude of selection-driven imbalance is pooled across non-randomised studies, but its direction is not transported between them.

"estimated"

\(\mu_\gamma\) is estimated, with the prior from baseline_difference_mean in set_priors().

The default is deliberate. Whether a treated group starts above or below its control is a property of each programme's targeting rule – some interventions go to high-need (high-baseline) populations, others to easy-to-reach (low-baseline) ones – not of the outcome or the intervention. Estimating a single \(\mu_\gamma\) asserts that a whole literature shares a direction of selection, and then applies that direction to every post-only study, whose own data cannot contradict it. Worse, the resulting bias does not shrink with more data: it sharpens, because \(\mu_\gamma\) is estimated more precisely. Set to "estimated" only when the studies plausibly share a targeting mechanism – for example, several evaluations of the same programme.

kappa

Excess-imbalance factor for randomised studies. Either a single non-negative number (default 0.5) or the string "estimate".

\(\kappa^2\) is the variance inflation of a randomised study's baseline contrast beyond simple random sampling, so \(\kappa^2 = \)DEFF\( - 1\) and \(\kappa = 0\) is perfect randomisation. Note \(\kappa = 0\) is not the same as ignoring finite-sample imbalance: the realised imbalance of a randomised allocation is already carried by the likelihood's \(\sigma^2/n\) terms (and, for DiD, propagated into the post period by the pre-post correlation). \(\kappa\) governs only the extra allowance for randomisation not having held exactly – imperfect allocation, attrition, post-randomisation selection.

Because \(s_i\) scales as \(1/\sqrt{n_i}\), this automatically down-weights small randomised studies more than large ones. For a post-only randomised study, where \(\gamma_i\) is unidentified, the mechanism is equivalent to inflating that study's standard error by \(\sqrt{1 + \kappa^2}\).

"estimate" samples \(\kappa\) with the prior from kappa in set_priors(), but by default is only permitted when at least one randomised study carries pre-treatment data (a randomised DiD). Post-only randomised studies constrain \(\kappa\) not at all. With no such anchor, either fix \(\kappa\) or set allow_unidentified_kappa = TRUE. The default of 0.5 is a reasonable central choice rather than a value to trust on its own, so it is worth refitting at a few values to see whether any conclusion turns on it.

cluster_deff_default

Design effect assumed for studies with randomisation = "cluster" that do not supply cluster_size and icc columns. Default 2, which corresponds to roughly 50 units per cluster at an ICC of 0.02. When both columns are supplied, the study's own \(1 + (m - 1)\rho_{ICC}\) is used instead. The design effect inflates \(s_i\) so that \(\kappa\) keeps one meaning across designs.

This corrects the baseline contrast only. A cluster-randomised study's likelihood still uses \(\sigma^2/n\) for the post-treatment period, so it remains over-precise about its own treatment effect. Correcting that needs cluster identifiers and a random effect, which this model does not carry.

covariates

An optional one-sided formula specifying study-level covariates for meta-regression on the treatment effect (e.g., ~ dose + year). The named columns must be numeric and present in both summary_data and individual_data (whichever are provided). For individual-level data, covariate values must be constant within each study. Default NULL (no meta-regression).

multiplicative_covariate

Optional specification of one or two categorical study-level covariates that modify the population treatment effect multiplicatively rather than additively. Either a single column name (character of length 1) for one covariate, or a one-sided formula naming one or two columns (~ a or ~ a + b). At most two are allowed. One factor is estimated per non-reference level of each covariate: studies at a covariate's reference level keep their population-mean linear predictor \(\mu_\theta + X_{\mathrm{cov},i}^{\top}\beta_{\mathrm{cov}}\) unchanged (factor fixed at 1), while studies at level \(k\) have it multiplied by the estimated effect_multiplier[k]. With two covariates the study's overall factor is the product of the two per-covariate factors, \(\alpha_{a(i)} \cdot \beta_{b(i)}\) — i.e. each covariate scales the effect independently (a log-additive structure). The reference level is the first factor level (declare the column as a factor to control it, with identical levels declared in every data frame), the lowest value for numeric input, or the alphabetically first value for character input. A numeric {0, 1} indicator is the simplest case: 0 is the reference (factor fixed at 1) and 1 selects the single estimated multiplier. Useful when a study attribute attenuates or amplifies the underlying effect by a shared factor — e.g. how an intervention was delivered, optionally crossed with a second attribute such as how long it ran. Each column must contain no NAs, be constant within study for individual-level data, must not also appear in covariates, and must take at least two distinct values across studies for its multipliers to be identified; the two columns must be distinct. Numeric columns with more than 5 distinct values are rejected as likely continuous (convert genuinely categorical numeric codes to a factor). The same multiplier prior from set_priors() is applied independently to every estimated factor. On the returned object, fit$multiplicative_covariate is a list with elements name and levels (reference first) for one covariate, or a list of two such descriptors for two covariates. Default NULL (no multiplicative structure).

center_covariates

Logical. If TRUE (default), covariates are mean-centered across all studies before fitting. This ensures that treatment_effect_mean is the population treatment effect at the average covariate values. Set to FALSE to use raw covariate values, in which case treatment_effect_mean is the effect when all covariates equal zero. The covariate coefficients (beta_cov) have the same interpretation regardless of centering: the change in expected treatment effect per unit increase in the covariate.

priors

A did_priors object from set_priors(). Controls the prior distributions on all population-level parameters.

method

Inference method. "sample" (default) runs full MCMC via Stan's HMC-NUTS sampler and returns a posterior distribution. "optimize" finds the maximum a posteriori (MAP) estimate via L-BFGS and is substantially faster, but returns only a point estimate with no uncertainty quantification.

chains

Number of MCMC chains. Ignored when method = "optimize". Default 4.

iter_warmup

Number of warmup iterations per chain. Ignored when method = "optimize". Default 1000.

iter_sampling

Number of sampling iterations per chain. Ignored when method = "optimize". Default 1000.

seed

Integer random seed for reproducibility. Default NULL.

allow_no_did

Logical. If FALSE (default), meta_did() will stop with an error when no DiD studies are present, because the treatment effect is not identified from the data without the double-difference structure. Set to TRUE to override this check if you understand the limitation (the posterior will be prior-driven).

allow_unidentified_kappa

Logical. If FALSE (default), kappa = "estimate" errors when no randomised study carries pre-treatment data, because \(\kappa\) is then not identified by anything. Set to TRUE to sample it anyway (the posterior for \(\kappa\) will reproduce its prior).

Doing so is a modelling choice rather than an estimate. Sampling \(\kappa\) instead of fixing it makes the marginal prior on \(\gamma_i\) a scale mixture of normals rather than a normal – simultaneously more peaked at zero and much heavier-tailed than any fixed \(\kappa\). That is a better description of "most randomised trials achieved balance, occasionally one badly did not" than a single scale can give, and it propagates the uncertainty in \(\kappa\) into the pooled effect rather than conditioning on one value. What it does not do is learn \(\kappa\) from the data, which is why it must be asked for explicitly.

...

Additional arguments passed to the underlying CmdStanModel method: $sample() when method = "sample" (e.g., parallel_chains, adapt_delta) or $optimize() when method = "optimize" (e.g., algorithm, iter).

Value

A meta_did_fit object. See print.meta_did_fit() and summary.meta_did_fit() for extracting results. When method = "optimize", the summary contains MAP point estimates only; sd, lo, and hi columns will be NA.

Details

DiD studies are required for identification of the treatment effect. Without them, the treatment effect is confounded with time trends (pre-post) or baseline group differences (RCT). See vignette("model-details") for a full discussion of the model, normalisation, and identification.

Examples

if (instantiate::stan_cmdstan_exists()) {
  studies <- data.frame(
    study_id            = c("Smith 2020", "Jones 2021"),
    design              = c("did", "rct"),
    n_control           = c(50, 60),
    mean_pre_control    = c(0.45, NA),
    mean_post_control   = c(0.42, 0.48),
    sd_pre_control      = c(0.12, NA),
    sd_post_control     = c(0.11, 0.12),
    n_treatment         = c(55, 65),
    mean_pre_treatment  = c(0.46, NA),
    mean_post_treatment = c(0.30, 0.35),
    sd_pre_treatment    = c(0.13, NA),
    sd_post_treatment   = c(0.10, 0.11),
    rho                 = c(0.75, NA)
  )
  fit <- meta_did(summary_data = studies)
}
#> No 'randomisation' column supplied, so all 1 post-only (RCT) studies are treated as non-randomised and have their baseline imbalance imputed from the other studies. That imputation subtracts directly from their estimated treatment effect.
#> Add a 'randomisation' column ("individual", "cluster" or "none") so randomised studies use the zero-centred, sample-size-scaled model instead. Silence with options(metadid.quiet = TRUE).
#> Running MCMC with 4 sequential chains...
#> 
#> Chain 1 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 1 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 1 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 1 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 1 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
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#> Chain 2 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: Exception: multi_normal_lpdf: Location parameter[2] is inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: Exception: multi_normal_lpdf: Location parameter[2] is inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
#> Chain 2 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 2 Exception: Exception: multi_normal_lpdf: Location parameter[2] is inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 2 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 2 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 2 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 2 
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#> Chain 3 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
#> Chain 3 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 3 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 3 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 3 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 3 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 3 
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#> Chain 4 Iteration:    1 / 2000 [  0%]  (Warmup) 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
#> Chain 4 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 4 Exception: Exception: multi_normal_lpdf: Location parameter[2] is -inf, but must be finite! (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model_functions.stan', line 49, column 2, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 8, column 2) (in '/home/runner/work/_temp/Library/00LOCK-metadid/00new/metadid/bin/stan/did_summary_model.stan', line 32, column 6, included from
#> Chain 4 '/tmp/RtmpgNfcyw/model-1eea1ba40a86.stan', line 51, column 2)
#> Chain 4 If this warning occurs sporadically, such as for highly constrained variable types like covariance matrices, then the sampler is fine,
#> Chain 4 but if this warning occurs often then your model may be either severely ill-conditioned or misspecified.
#> Chain 4 
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#> Chain 4 finished in 11.0 seconds.
#> 
#> All 4 chains finished successfully.
#> Mean chain execution time: 8.8 seconds.
#> Total execution time: 35.5 seconds.
#> 
#> Warning: 830 of 4000 (21.0%) transitions ended with a divergence.
#> See https://mc-stan.org/misc/warnings for details.
#> Warning: 2517 of 4000 (63.0%) transitions hit the maximum treedepth limit of 10.
#> See https://mc-stan.org/misc/warnings for details.