corlatent {latentgraph} | R Documentation |
Estimate graphical models with latent variables and correlated replicates using the method in Jin et al. (2020).
corlatent(data, accuracy, n, R, p, lambda1, lambda2, lambda3, distribution = "Gaussian",
rule = "AND")
data |
data set. Can be a matrix, list, array, or data frame. If the data set is a matrix, it should have |
accuracy |
the threshhold where algorithm stops. The algorithm stops when the difference between estimaters of the |
n |
the number of observations. |
R |
the number of replicates for each observation. |
p |
the number of observed variables. |
lambda1 |
tuning parameter that encourages estimated graph to be sparse. |
lambda2 |
tuning parameter that models the effects of correlated replicates. Usually set to be equal to lambda1. |
lambda3 |
tuning parameter that encourages the latent effect to be piecewise constants. |
distribution |
For a data set with Gaussian distribution, use "Gaussian"; For a data set with Ising distribution, use "Ising". Default is "Gaussian". |
rule |
rules to combine matrices that encode the conditional dependence relationships between sets of two observed variables. Options are "AND" and "OR". Default is "AND". |
The corlatent method has two assumptions. Assumption 1 states that the R
replicates are assumed to follow a one-lag vector autoregressive model, conditioned on the latent variables.
Assumption 2 states that the latent variables are piecewise constant across replicates.
Based on these two assumptions, the method solve the following problem for 1 \le j \le p
.
\min_{\theta_{j,-j}, \alpha_j, \Delta_j} \{ -\frac{1}{nR}l(\theta_{j,-j}, \alpha_j, \Delta_j) + \lambda\|\theta_{j,-j}\|_1 + \beta\|\alpha_j\|_1 + \gamma\|(I_n \otimes C)\Delta_j\|_1 \},
where l(\theta_{j,-j}, \alpha_j, \Delta_j)
is the log likelihood function, \theta_{j,-j}
encodes the conditional dependence relationships between j
th observed variable and the other observed variables, \alpha_j
models the correlation among replicates, \Delta_j
encodes the latent effect, \lambda
, \beta
, \gamma
are the tuning parameters, I_n
is an n-dimensional identity matrix and C
is the discrete first derivative matrix where the i
th and (i+1)
th column of every ith row are -1 and 1, respectively.
This method aims at modeling exponential family graphical models with correlated replicates and latent variables.
omega |
a matrix that encodes the conditional dependence relationships between sets of two observed variables |
theta |
the adjacency matrix with 0 and 1 encoding conditional independence and dependence between sets of two observed variables, respectively |
penalties |
the penalty values |
Jin, Y., Ning, Y., and Tan, K. M. (2020), ‘Exponential Family Graphical Models with Correlated Replicates and Unmeasured Confounders’, preprint available.
# Gaussian distribution with "AND" rule
n <- 20
R <- 10
p <- 5
l <- 2
s <- 2
seed <- 1
data <- generate_Gaussian(n, R, p, l, s, sparsityA = 0.95, sparsityobserved = 0.9,
sparsitylatent = 0.2, lwb = 0.3, upb = 0.3, seed)$X
result <- corlatent(data, accuracy = 1e-6, n, R, p,lambda1 = 0.1, lambda2 = 0.1,
lambda3 = 1e+5,distribution = "Gaussian", rule = "AND")