# Fit LUCID models with one or multiple omics layers EM algorithm to estimate LUCID with one or multiple omics layers ```r estimate_lucid( lucid_model = c("early", "parallel", "serial"), G, Z, Y, CoG = NULL, CoY = NULL, K, init_omic.data.model = "EEV", useY = TRUE, tol = 0.001, max_itr = 1000, max_tot.itr = 10000, Rho_G = 0, Rho_Z_Mu = 0, Rho_Z_Cov = 0, family = c("normal", "binary"), seed = 123, init_impute = c("mix", "lod"), init_par = c("mclust", "random"), verbose = FALSE ) ``` ## Arguments - `lucid_model`: Specifying LUCID model, "early" for early integration, "parallel" for lucid in parallel, "serial" for lucid in serial - `G`: an N by P matrix representing exposures - `Z`: Omics data, if "early", an N by M matrix; If "parallel", a list, each element i is a matrix with N rows and P_i features; If "serial", a list, each element i is a matrix with N rows and p_i features or a list with two or more matrices with N rows and a certain number of features - `Y`: a length N vector - `CoG`: an N by V matrix representing covariates to be adjusted for G -> X - `CoY`: an N by K matrix representing covariates to be adjusted for X -> Y - `K`: Number of latent clusters. If "early", an integer greater or equal to 2; If "parallel",an integer vector, same length as Z, with each element being an interger greater or equal to 2; If "serial", a list, each element is either an integer like that for "early" or an list of integers like that for "parallel", same length as Z - `init_omic.data.model`: a vector of strings specifies the geometric model of omics data. If NULL, See more in ?mclust::mclustModelNames - `useY`: logical, if TRUE, EM algorithm fits a supervised LUCID; otherwise unsupervised LUCID. - `tol`: stopping criterion for the EM algorithm - `max_itr`: Maximum iterations of the EM algorithm. If the EM algorithm iterates more than max_itr without converging, the EM algorithm is forced to stop. - `max_tot.itr`: Max number of total iterations for `estimate_lucid` function. `estimate_lucid` may conduct EM algorithm for multiple times if the algorithm fails to converge. - `Rho_G`: A scalar. This parameter is the LASSO penalty to regularize exposures. If user wants to tune the penalty, use the wrapper function `lucid`. Now only achieved for LUCID early integration. - `Rho_Z_Mu`: A scalar. This parameter is the LASSO penalty to regularize cluster-specific means for omics data (Z). If user wants to tune the penalty, use the wrapper function `lucid`.Now only achieved for LUCID early integration. - `Rho_Z_Cov`: A scalar. This parameter is the graphical LASSO penalty to estimate sparse cluster-specific variance-covariance matrices for omics data (Z). If user wants to tune the penalty, use the wrapper function `lucid`. Now only achieved for LUCID early integration. - `family`: The distribution of the outcome - `seed`: Random seed to initialize the EM algorithm - `init_impute`: Method to initialize the imputation of missing values in LUCID. `mix` will use `mclust:imputeData` to implement EM Algorithm for Unrestricted General Location Model by the mix package to impute the missing values in omics data; `lod` will initialize the imputation via replacing missing values by LOD / sqrt(2). LOD is determined by the minimum of each variable in omics data. - `init_par`: For "early", an interface to initialize EM algorithm, if mclust, initiate the parameters using the `mclust` package, if random, initiate the parameters by drawing from a uniform distribution; For "parallel", mclust is the default for quick convergence; For "serial", each sub-model follows the above depending on it is a "early" or "parallel" - `verbose`: A flag indicates whether detailed information for each iteration of EM algorithm is printed in console. Default is FALSE. ## Returns A list contains the object below: 1. res_Beta: estimation for G-\>X associations 2. res_Mu: estimation for the mu of the X-\>Z associations 3. res_Sigma: estimation for the sigma of the X-\>Z associations 4. res_Gamma: estimation for X-\>Y associations 5. inclusion.p: inclusion probability of cluster assignment for each observation 6. K: umber of latent clusters for "early"/list of numbers of latent clusters for "parallel" and "serial" 7. var.names: names for the G, Z, Y variables 8. init_omic.data.model: pre-specified geometric model of multi-omics data 9. likelihood: converged LUCID model log likelihood 10. family: the distribution of the outcome 11. select: for LUCID early integration only, indicators of whether each exposure and omics feature is selected 12. useY: whether this LUCID model is supervised 13. Z: multi-omics data 14. init_impute: pre-specified imputation method 15. init_par: pre-specified parameter initialization method 16. Rho: for LUCID early integration only, pre-specified regularity tuning parameter 17. N: number of observations 18. submodel: for LUCID in serial only, storing all the submodels ## Examples ```r i <- 1008 set.seed(i) G <- matrix(rnorm(500), nrow = 100) Z1 <- matrix(rnorm(1000),nrow = 100) Z2 <- matrix(rnorm(1000), nrow = 100) Z3 <- matrix(rnorm(1000), nrow = 100) Z4 <- matrix(rnorm(1000), nrow = 100) Z5 <- matrix(rnorm(1000), nrow = 100) Z <- list(Z1 = Z1, Z2 = Z2, Z3 = Z3, Z4 = Z4, Z5 = Z5) Y <- rnorm(100) CoY <- matrix(rnorm(200), nrow = 100) CoG <- matrix(rnorm(200), nrow = 100) fit1 <- estimate_lucid(G = G, Z = Z, Y = Y, K = list(2,2,2,2,2), lucid_model = "serial", family = "normal", seed = i, CoG = CoG, CoY = CoY, useY = TRUE) ```

estimate_lucid function