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Maltiel et al (2015) Combined Model

maltiel_cm.Rd

Bayesian model for ARD with both barrier effect and transmission bias parameters.

  • maltiel_cm_count – combined model for count responses, as described in section 2.4 of Maltiel et al (2015). It carries both the per-sub-population overdispersion rho_k of the barrier effects model and the transmission bias tau_k of the transmission bias model: y_ik ~ Binomial(d_i, tau_k * q_ik) with d_i ~ LogNormal(mu, sigma^2) and q_ik ~ Beta(m_k, rho_k). Multiplying q_ik by tau_k breaks the Beta-Binomial conjugacy, so – unlike maltiel_bem_count() – the latent q_ik cannot be integrated out and are sampled together with the remaining parameters. This adds N * K parameters, so fits are substantially slower than for the component models.

Usage

maltiel_cm_count(N, K, y, m, L, eta, v, ...)

Arguments

N

integer; population size

K

integer; number of sub-populations

y

numeric matrix; ARD counts (N x K)

m

numeric vector; fractional sub-population sizes (length K)

L

numeric vector; lower bounds on individual degrees (length N). Must satisfy L[i] >= max(y[i,]) for each respondent i so that the degree is always at least as large as the maximum observed count.

eta

numeric vector; Beta prior shape 1 for each transmission bias (length K)

v

numeric vector; Beta prior shape 2 for each transmission bias (length K)

...

other arguments passed to cmdstanr::sample()

Value

Object of class cmdstanr::CmdStanMCMC containing the samples.

Details

Calling this function(s) will load the model object using get_model() and sample from the posterior using the cmdstanr::sample() method.

The transmission biases tau_k and the degrees d_i are only weakly identified from ARD alone: scaling tau_k down and the degrees up leaves the reported counts largely unchanged. The eta / v prior on tau is what resolves this, so an uninformative eta = v = 1 will typically pull the posterior for tau below 1 and inflate the estimated degrees. Supply an informative prior reflecting what is known about transmission for each sub-population.

References

Maltiel, R., Raftery, A. E., McCormick, T. H., & Baraff, A. J. (2015). Estimating Population Size Using the Network Scale Up Method. The Annals of Applied Statistics, 9(3), 1247–1277. doi:10.1214/15-AOAS827

See also

Use get_model() to return Stan model object of class cmdstanr::CmdStanModel without fitting it.

Other models in this package: maltiel_bem, maltiel_rdm, maltiel_tbm, test_model(), zheng_bem, zheng_gp

Other models of Maltiel et al (2015): maltiel_bem, maltiel_rdm, maltiel_tbm

Examples

data("Fake_maltiel_RD", package = "stansum")
y <- data.matrix(Fake_maltiel_RD)[1:50, ]
K <- ncol(y)
r <- maltiel_cm_count(
  N = nrow(y),
  K = K,
  y = y,
  m = rep(0.01, K),
  L = apply(y, 1, max),
  eta = rep(1, K),
  v = rep(1, K),
  chains = 1,
  iter_warmup = 200,
  iter_sampling = 10
)
#> Running MCMC with 1 chain...
#> 
#> Chain 1 Iteration:   1 / 210 [  0%]  (Warmup) 
#> Chain 1 Informational Message: The current Metropolis proposal is about to be rejected because of the following issue:
#> Chain 1 Exception: beta_lpdf: First shape parameter is 0, but must be positive finite! (in '/tmp/RtmpnudLi4/model-3495457c83bf.stan', line 37, column 4 to column 74)
#> 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: beta_lpdf: First shape parameter is 0, but must be positive finite! (in '/tmp/RtmpnudLi4/model-3495457c83bf.stan', line 37, column 4 to column 74)
#> 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: beta_lpdf: First shape parameter is 0, but must be positive finite! (in '/tmp/RtmpnudLi4/model-3495457c83bf.stan', line 37, column 4 to column 74)
#> 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 Iteration: 100 / 210 [ 47%]  (Warmup) 
#> Chain 1 Iteration: 200 / 210 [ 95%]  (Warmup) 
#> Chain 1 Iteration: 201 / 210 [ 95%]  (Sampling) 
#> Chain 1 Iteration: 210 / 210 [100%]  (Sampling) 
#> Chain 1 finished in 0.5 seconds.