lsirm1pl_normal_ss {lsirm12pl} | R Documentation |
1pl LSIRM model with normal likelihood and model selection approach.
Description
lsirm1pl_normal_ss is used to fit LSIRM model with model selection approach based on spike-and-slab priors for continuous variable with 1pl. LSIRM factorizes continuous item response matrix into column-wise item effect, row-wise respondent effect and further embeds interaction effect in a latent space. The resulting latent space provides an interaction map that represents interactions between respondents and items.
Usage
lsirm1pl_normal_ss(
data,
ndim = 2,
niter = 15000,
nburn = 2500,
nthin = 5,
nprint = 500,
jump_beta = 0.4,
jump_theta = 1,
jump_gamma = 1,
jump_z = 0.5,
jump_w = 0.5,
pr_mean_beta = 0,
pr_sd_beta = 1,
pr_mean_theta = 0,
pr_spike_mean = -3,
pr_spike_sd = 1,
pr_slab_mean = 0.5,
pr_slab_sd = 1,
pr_a_theta = 0.001,
pr_b_theta = 0.001,
pr_a_eps = 0.001,
pr_b_eps = 0.001,
pr_xi_a = 0.001,
pr_xi_b = 0.001,
verbose = FALSE
)
Arguments
data |
Matrix; continuous item response matrix to be analyzed. Each row is assumed to be respondent and its column values are assumed to be response to the corresponding item. |
ndim |
Numeric; dimension of latent space. default value is 2. |
niter |
Numeric; number of iterations to run MCMC sampling. default value is 15000. |
nburn |
Numeric; number of initial, pre-thinning, MCMC iterations to discard. default value is 2500. |
nthin |
Numeric;number of thinning, MCMC iterations to discard. default value is 5. |
nprint |
Numeric; MCMC samples is displayed during execution of MCMC chain for each |
jump_beta |
Numeric; jumping rule of the proposal density for beta. default value is 0.4. |
jump_theta |
Numeric; jumping rule of the proposal density for theta. default value is 1.0. |
jump_gamma |
Numeric; jumping rule of the proposal density for gamma. default value is 0.025. |
jump_z |
Numeric; jumping rule of the proposal density for z. default value is 0.5. |
jump_w |
Numeric; jumping rule of the proposal density for w. default value is 0.5. |
pr_mean_beta |
Numeric; mean of normal prior for beta. default value is 0. |
pr_sd_beta |
Numeric; standard deviation of normal prior for beta. default value is 1.0. |
pr_mean_theta |
Numeric; mean of normal prior for theta. default value is 0. |
pr_spike_mean |
Numeric; mean of spike prior for log gamma default value is -3. |
pr_spike_sd |
Numeric; standard deviation of spike prior for log gamma default value is 1. |
pr_slab_mean |
Numeric; mean of spike prior for log gamma default value is 0.5. |
pr_slab_sd |
Numeric; standard deviation of spike prior for log gamma default value is 1. |
pr_a_theta |
Numeric; shape parameter of inverse gamma prior for variance of theta. default value is 0.001. |
pr_b_theta |
Numeric; scale parameter of inverse gamma prior for variance of theta. default value is 0.001. |
pr_a_eps |
Numeric; shape parameter of inverse gamma prior for variance of data likelihood. default value is 0.001. |
pr_b_eps |
Numeric; scale parameter of inverse gamma prior for variance of data likelihood default value is 0.001. |
pr_xi_a |
Numeric; first shape parameter of beta prior for latent variable xi. default value is 1. |
pr_xi_b |
Numeric; second shape parameter of beta prior for latent variable xi. default value is 1. |
verbose |
Logical; If TRUE, MCMC samples are printed for each |
Details
lsirm1pl_normal_ss
models the continuous value of response by respondent j
to item i
with item effect \beta_i
, respondent effect \theta_j
and the distance between latent position w_i
of item i
and latent position z_j
of respondent j
in the shared metric space, with \gamma
represents the weight of the distance term:
Y_{j,i} = \theta_j+\beta_i-\gamma||z_j-w_i|| + e_{j,i}
where the error e_{j,i} \sim N(0,\sigma^2)
. lsrm1pl_noraml_ss
model include model selection approach based on spike-and-slab priors for log gamma. For detail of spike-and-slab priors, see References.
Value
lsirm1pl_normal_ss
returns an object of list containing the following components:
data |
data frame or matrix containing the variables in the model. |
bic |
Numeric value with the corresponding BIC. |
mcmc_inf |
number of mcmc iteration, burn-in periods, and thinning intervals. |
map_inf |
value of log maximum a posterior and iteration number which have log maximum a posterior. |
beta_estimate |
posterior estimation of beta. |
theta_estimate |
posterior estimation of theta. |
sigma_theta_estimate |
posterior estimation of standard deviation of theta. |
sigma_estimate |
posterior estimation of standard deviation. |
gamma_estimate |
posterior estimation of gamma. |
z_estimate |
posterior estimation of z. |
w_estimate |
posterior estimation of w. |
pi_estimate |
posterior estimation of phi. inclusion probability of gamma. if estimation of phi is less than 0.5, choose Rasch model with gamma = 0, otherwise latent space model with gamma > 0. |
beta |
posterior samples of beta. |
theta |
posterior samples of theta. |
theta_sd |
posterior samples of standard deviation of theta. |
sigma |
posterior samples of standard deviation. |
gamma |
posterior samples of gamma. |
z |
posterior samples of z. The output is 3-dimensional matrix with last axis represent the dimension of latent space. |
w |
posterior samples of w. The output is 3-dimensional matrix with last axis represent the dimension of latent space. |
pi |
posterior samples of phi which is indicator of spike and slab prior. If phi is 1, log gamma follows the slab prior, otherwise follows the spike prior. |
accept_beta |
accept ratio of beta. |
accept_theta |
accept ratio of theta. |
accept_w |
accept ratio of w. |
accept_z |
accept ratio of z. |
accept_gamma |
accept ratio of gamma. |
References
Ishwaran, H., & Rao, J. S. (2005). Spike and slab variable selection: Frequentist and Bayesian strategies (Vol. 33). The Annals of Statistics
Examples
# generate example (continuous) item response matrix
data <- matrix(rnorm(500, mean = 0, sd = 1),ncol=10,nrow=50)
lsirm_result <- lsirm1pl_normal_ss(data)
# The code following can achieve the same result.
lsirm_result <- lsirm(data ~ lsirm1pl(spikenslab = TRUE, fixed_gamma = FALSE))