# Compute Log-Likelihood Ratio test statistics for permutation based Extended Random Effect Maximal Interaction (E-ReMI) Two-Mode Clustering Model Computes the log-likelihood ratio statistic used for hypothesis testing in the E-ReMI for Two-Mode Clustering model. The statistic compares the fitted model (some intercation) against a null model (no intercation). ```r Log_LR_Test_Statistic(DC, I, J, initM, initOmega_hat) ``` ## Arguments - `DC`: A numeric data matrix of size `I x J`, typically doubly centered, representing the two-mode data to be analyzed. - `I`: An integer specifying the number of rows (first mode entities) in the data matrix. - `J`: An integer specifying the number of columns (second mode entities) in the data matrix. - `initM`: The matrix M is reconstructed obtained via initial random row partition matrix (R), initial random column partition matrix (C) and initial bi-cluster interaction matrix (G) and it is updated after each updation of R, C and G. - `initOmega_hat`: A numeric vector of estimated row cluster weights (proportions), summing to 1. ## Details This function evaluates the log-likelihood ratio (LLR) test statistic by comparing the log-likelihood under the fitted model (presence of row by colum cluster intercation) to that of a baseline model with no intercation. The test statistic can be used in permutation-based inference procedures to assess significance of row by colum cluster intercation in two-mode data. ## Returns Returns a single numeric value: - **Log_LR**: The value of the log-likelihood ratio test statistic. ## References Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2025). Robustness study of normality-based likelihood ratio tests for testing maximal interaction two-mode clustering and a permutation based alternative. **Available on OSF** (submitted to Advances in Data Analysis and Classification). Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2023). E-ReMI: extended maximal interaction two-mode clustering. **Journal of Classification, 40, 298-331** Ahmed, Z., van Breukelen, G. J. P., Schepers, J., & Cassese, A. (2021). REMAXINT: a two-mode clustering-based method for statistical inference on two-way interaction. **Advances in Data Analysis and Classification, 15(4), 987-1013** ## Author(s) Zaheer Ahmed (ahmed@ifado.de), Jan Schepers (jan.schepers@maastrichtuniversity.nl), Uwe Ligges (ligges@statistik.tu-dortmund.de), Alberto Cassese (alberto.cassese@unifi.it), Gerard van Breukelen (gerard.vbreukelen@maastrichtuniversity.nl), Katja Ickstadt (ickstadt@statistik.tu-dortmund.de), Edmund Wascher (wascher@ifado.de) ## Note Used internally in permutation-based hypothesis testing procedures for the E-ReMI Two-Mode Clustering framework. ## See Also `Permutation_Function, diag, pinv` ## Examples ```r I <- 10; P <- 4; J <- 5; Q <- 2 DC <- matrix(rnorm(I*J), I, J) R <- diag(1, I, P) C <- diag(1, J, Q) R_inv <- pracma::pinv(t(R) %*% R) C_inv <- pracma::pinv(t(C) %*% C) G <- R_inv %*% t(R) %*% DC %*% C %*% C_inv initM <- R %*% G %*% t(C) initOmega_hat <- c(0.5, rep((1-0.5)/P, P)) result <- Log_LR_Test_Statistic(DC, I, J, initM, initOmega_hat) result ```

Log_LR_Test_Statistic function