{"id":"9f98cead-fb97-434b-9583-4e4ec6cb5cf9","arxiv_id":"1908.04020","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"mixed-SCGLR combines supervised component-based regression with Schall's algorithm to fit regularized multivariate generalized linear mixed models on grouped data.","lead":"Researchers extend the SCGLR method for building a few interpretable components from many redundant predictors to grouped data with random effects, calling the result mixed-SCGLR. The method provides regularized estimates and interpretable component planes for multivariate generalized linear mixed models, with simulations and a forest ecology application.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The component criterion in Algorithm 1 projects the working variable including the random-effects term onto the X-space, so supervised components can become confounded with group-level variation and bias the fixed-effect estimates.","rationale":"The reader's weakest assumption was the Schall/PQL-type linearisation and its potential to bias variance components and hence the whole procedure. My concern is related but more specific: the component extraction criterion in Eq. (10) is not merely using an approximate linearisation; it evaluates the goodness-of-fit of the working vector z^ξ in the metric W^ξ while omitting the random-effects covariance U D U^T. Because z^ξ includes the estimated random-effect term, the projection onto span{Xu, A} can be inflated by group-level variation. This is an internal mismatch between the objective used to build components and the model used to estimate parameters, and it hits the central claims of both fixed-effect accuracy and interpretability. The paper's simulations do not include group-level confounding of X, so the evidence provided does not rule the issue out. The manuscript has real strengths: it supplies an R package, reproducible simulation code, and honest self-reported limitations in Sections 6.2 and 7, including non-convergence for s near 0 and binary-data variance bias. Those strengths do not resolve this concern, because the simulations are generated in a regime where U and X are independent. A single targeted simulation with correlated group-mean structure, as proposed in the concrete test, would settle whether the omitted random-effects term in the component criterion is a practical problem or only a theoretical one. If the test shows large contamination, the method would need an additional orthogonalisation or residualisation step before the central claims can be accepted broadly; if the test shows negligible change, the current algorithm is empirically robust to the objection. This reasoning leaves the reader's CONDITIONAL verdict unchanged: the method is promising and well-supported in the tested regime, but the component-criterion mismatch should be resolved before general adoption.","tokens_in":26720,"tokens_out":19753,"duration_ms":209548,"concrete_test":"Simulate grouped data from the Gaussian scheme of Section 5.1, but generate X with group-level means correlated with the random effects: for each bundle variable x_j, set x_j = φ + Uα_j + ε_j, with the true fixed-effect component defined on within-group centred variables and non-zero α_j on nuisance variables. Run the current mixed-SCGLR and a modified version in which Step 1 uses z^ξ_k − Uξ_k (or the residual after projecting out U) inside ψ_A, keeping all other steps identical. If the cosine between the first component and the true within-group direction decreases materially, or the MURSE for fixed effects increases, under the current algorithm but not under the modified version, the concern is confirmed. As a complementary check on the real data, compute the norm of U^T W^ξ X at convergence; if it is far from zero, the confounding is active in the Genus application.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that mixed-SCGLR recovers accurate fixed-effect estimates and interpretable components for grouped data. The load-bearing step is Algorithm 1 Step 1, which maximises the goodness-of-fit criterion in Eq. (10): ψ_A(u) = Σ_k ||z^ξ_k||²_{W^ξ_k} cos²_{W^ξ_k}(z^ξ_k, span{Xu, A}). However, the linearised model in Eq. (9) is z^ξ_k = (Xu)γ_k + Aδ_k + Uξ_k + e_k, with conditional covariance W^{ξ-1}_k. The criterion uses only the conditional weight W^ξ_k and projects z^ξ_k — which contains Uξ_k — onto span{Xu, A}. The marginal covariance of z^ξ_k is W^{ξ-1}_k + U D_k U^T, not W^{ξ-1}_k. Unless U^T W^ξ_k X = 0 and U^T W^ξ_k A = 0 (not implied by the model), the projection of Uξ_k onto span{Xu, A} contributes to ψ_A and depends on u. The maximiser of ψ_A can therefore align Xu with group-mean variation attributable to random effects rather than with the fixed structural relationship. Since Step 2 then estimates γ_k, δ_k and ξ_k jointly from the Henderson system, this contamination propagates into the reported fixed-effect accuracy and into the interpretation of components. The Gaussian simulations generate X independently of Uξ, which masks the issue; the forest concession data, with plots grouped into 22 concessions, is exactly the setting where group-level confounding is plausible. The paper's own Section 7 note that binary-data variance components are biased toward zero points to the same under-specification of random effects in the working criterion, but the component-objection mismatch here is more direct.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends Supervised Component-based Generalised Linear Regression (SCGLR) to multivariate generalized linear mixed models for grouped data. The proposed mixed-SCGLR method models q responses with linear predictors η_k = (Xu)γ_k + Aδ_k + Uξ_k, where X contains many redundant predictors, A contains few covariates of interest, and U is the random-effects design matrix. Estimation alternates between: (i) computing supervised components by maximizing a criterion that combines structural relevance and the goodness-of-fit of Schall's linearised working variables; (ii) solving Henderson systems for fixed effects, random effects, and variance components; and (iii) updating working variables and weights. Higher-rank components are extracted under orthogonality constraints via the PING algorithm. The method is evaluated on extensive simulations with Gaussian, Bernoulli, Poisson, and binomial outcomes, on high-dimensional settings, and on a forest ecology dataset with 22 concessions, and is compared with ridge and LASSO regularisations. The main claims are that mixed-SCGLR yields accurate fixed-effect estimates and interpretable components for grouped data, and that accounting for within-group dependence improves prediction over SCGLR.","tokens_in":27100,"tokens_out":6445,"duration_ms":70385,"significance":"The problem addressed is practically important: regularised regression for non-independent grouped data with many redundant predictors is common in ecology, epidemiology, and social science. If the central claims hold, mixed-SCGLR is a useful addition to the toolbox, especially because it provides interpretable supervised components in a GLMM setting where L1/L2 penalised methods are less interpretable. The paper's strengths include a clearly specified algorithm, extensive simulations covering several response distributions and high-dimensional cases, a real-data application, and the release of R code and a package. The PING algorithm is given in supplementary material. The main caveat is that the component criterion uses Schall working variables that contain the random-effects term, and no mechanism guarantees that this term does not influence the selected component directions. This issue is addressable and the central idea is defensible, so the paper merits revision rather than rejection.","major_comments":[{"comment":"The goodness-of-fit criterion ψ_A(u) projects the working variable z^ξ_k, which satisfies z^ξ_k = (Xu)γ_k + Aδ_k + Uξ_k + e_k, onto span{Xu,A} using the conditional metric W^ξ_k. The marginal covariance of z^ξ_k is W^{ξ-1}_k + U D_k U^T, not W^{ξ-1}_k. Unless U^T W^ξ_k X u = 0 and U^T W^ξ_k A = 0, which the model does not imply, the random-effect term Uξ_k contributes to the projection and this contribution depends on u. Consequently, the component selected by (10) can be aligned with group-level variation rather than with the fixed structural relationship, and this potential contamination is inherited by the Henderson-system estimates in Step 2. The Gaussian simulations in Section 5.1 generate X independently of ξ, which may understate the problem; the real-data setting in Section 6, with plots grouped into 22 concessions, is exactly a setting where group-level confounding is plausible. Please address this by either modifying the criterion, for example by using the marginal covariance of the working variable or by projecting out the random-effect subspace, or by providing additional simulations in which X has group structure or is correlated with the random effects, together with a discussion of the sensitivity of the fixed-effect estimates.","section":"Section 4.1.2, Eq. (10) and Algorithm 1 Step 1"},{"comment":"The simulation comparisons report only point estimates of MURSE and MRSE over B=100 samples, with no standard errors, confidence intervals, or Monte Carlo error estimates. Some of the reported differences are small relative to what one would expect from 100 replications; for example, Table 2 shows MURSE 0.10 for mixed-SCGLR versus 0.13 for LMM-ridge at τ=0.3, and Table 3 shows a Poisson MRSE of 0.30 for GLMM-LASSO versus 0.46 for mixed-SCGLR at τ=0.1. The same issue affects the supplementary tables. Since the ordering claims are central to the paper's conclusions, please add Monte Carlo standard errors or confidence intervals for the main comparisons, or at least for the entries that support the claimed ordering.","section":"Section 5.3, Tables 2 and 3"},{"comment":"No convergence guarantee or detailed convergence diagnostics are provided for the alternating algorithm. The stopping rule is described as iteration 'until stability of parameters is reached', but the tolerance, the maximum number of iterations, and the failure rate across the B=100 simulation replications are not reported. Section 6.2 notes non-convergence for s=0, which indicates that convergence behaviour is not automatic. Because the method's output, and hence the accuracy and interpretation claims, depends on this iteration, please add empirical convergence diagnostics (for example, the number of runs that reached the stated tolerance and the distribution of the number of iterations) and, if possible, a local convergence argument for the combined criterion maximised in Step 1.","section":"Section 4.2, Algorithm 1"}],"minor_comments":[{"comment":"In the displayed Henderson system of Algorithm 1, the off-diagonal blocks involving A^T W f and U^T W f use f^{[t]} while the first row and the diagonal blocks use f^{[t+1]}; this is presumably a typo and should use f^{[t+1]} consistently throughout the matrix.","section":"Algorithm 1, Step 2"},{"comment":"The notation in Eq. (10) omits the iteration index [t] that is used elsewhere in Algorithm 1; adding these superscripts would make the dependence of ψ_A on the current working variables and weights explicit and easier to check.","section":"Section 4.1.2, Eq. (10)"},{"comment":"The acknowledged bias toward zero of variance-component estimates for binary outcomes should be connected to the role of D_k in Algorithm 1. Since D_k enters the Henderson system and the variance-component update, an underestimated σ_k^2 will affect the next iteration's working variables and weights; a brief discussion of this propagation, or a diagnostic in the Bernoulli simulations, would help the reader judge the practical impact.","section":"Section 7"},{"comment":"The cross-validation procedure is described as 'leave-two-observations-out per group' with five parts, but the paper does not report the variability of the selected tuning parameters s*, K*, and λ* across the 100 samples; reporting, for example, the observed range of K* and the standard deviation of s* would strengthen the calibration discussion.","section":"Section 5.2 and supplementary material"},{"comment":"The reference to Bry et al. (2018) is given as 'In press'; if the paper has since been published, please update the citation with the journal, volume, and pages.","section":"References"},{"comment":"Figure 3 contains many overlapping curves and is difficult to read, especially for intermediate values of s; a small multiple of panels or a heatmap of the cross-validation error over the (s,l) grid would be clearer.","section":"Figure 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is an incremental but potentially useful extension of the authors' own SCGLR framework. The main novelty is the integration of random effects into the component-based regularisation scheme. My main concern is the construction of the goodness-of-fit criterion in Eq. (10): projecting a working variable that contains the random-effects term onto the fixed-effect space, using only the conditional weight matrix, creates a real risk of confounding component directions with group-level variation. This is not a circularity issue, but it is a correctness-risk issue in the central claim about fixed-effect accuracy. I would like to see either a modification of the criterion or convincing simulations with group-structured or random-effect-correlated X before publication. The missing Monte Carlo error bars in the simulation comparisons also need attention, as several of the reported advantages are modest. The availability of code and the real-data application are clear strengths."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper extends SCGLR to generalized linear mixed models by embedding Schall's linearisation in the component-search step. The extension is natural within the authors' own SCGLR program, and they do it carefully: they supply a new optimisation routine (PING), an R package, extensive simulations across Gaussian, Bernoulli, Poisson and binomial outcomes, a high-dimensional variant, and a realistic forest ecology application. That is real work, and the simulations show a clear advantage over ridge and LASSO when predictors are collinear and grouped. The interpretation plots are a genuine strength.\n\nThe main soft spots are not fatal, but they are real. First, Algorithm 1, Step 2 has a visible indexing inconsistency: the Henderson system mixes f[t+1] on the diagonal and right-hand side with f[t] in some off-diagonal blocks. That is likely a typo, but it needs to be fixed before the algorithm can be implemented unambiguously. Second, there is no convergence proof for the alternating scheme or for PING; the authors present only an ascent-step argument. For a heuristic component method this is acceptable, but it should be stated plainly as an open question. Third, the simulation comparisons report MURSE and MRSE as point values over 100 samples, with no standard errors or intervals; the headline claims rest on single numbers.\n\nThe deeper concern, and one I want you to weigh carefully, is that the component criterion in Eq. (10) projects the working variable z_k (which contains U_k ξ_k) onto span{Xu, A} using only the conditional weight matrix. The marginal covariance of z is W^{-1} + U D U^T, not W^{-1}, so random-effect variation can leak into the component direction. The simulations generate X independently of the random effects, which masks the issue. In the forest data, with plots grouped into concessions and environmental predictors varying at group level, the components might partly capture group-mean differences rather than fixed structural effects. The paper never discusses this. It is not a fatal flaw—the method still works in practice—but it should be addressed, perhaps by orthogonalising z with respect to U or by adopting a marginalised criterion.\n\nThe paper is honest: Section 7 admits the binary-data variance bias and the risk of non-convergence for small s. The citation pattern is appropriate, with self-citations to prior SCGLR work that is legitimate. Overall, this is a useful contribution for applied statisticians working with grouped, collinear, multivariate responses. It deserves a serious referee, and with those fixes and a clearer discussion of the random-effects confounding, I would be happy to see it published.","headline":"A solid, honest extension of SCGLR to GLMMs, but the method is heuristic and the component criterion may confound random effects with fixed structure.","tokens_in":27636,"tokens_out":3350,"would_cite":false,"duration_ms":40256,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["62J12","62H25","62J07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Mixed-SCGLR extends supervised-component regression to grouped-data GLMMs, recovering latent predictor bundles while regularising the fixed effects.","keywords":["generalized linear mixed models","supervised components","component-based regularization","structural relevance","Schall's algorithm","multivariate GLMM","grouped data","PLS-type methods"],"falsifier":"Simulate grouped binary data from a known latent structure, fit the same data with mixed-SCGLR and with a GLMM estimated by adaptive Gauss-Hermite quadrature, and compare the first estimated component direction and the variance-component estimate across many replications; if the component direction shifts materially while the variance-component estimate is biased toward zero, Schall's linearisation is the approximation that needs replacing.","tokens_in":26514,"feed_emoji":"🌲","tokens_out":10422,"duration_ms":97433,"temperature":0.7,"pith_summary":"Mixed-SCGLR extends the supervised-component regression method SCGLR to multivariate generalised linear mixed models, so that grouped data can be modelled while the many redundant explanatory variables are compressed into a few supervised components. The paper's central claim is that this component-based regularisation is more accurate than ridge or LASSO regularisation when the true explanatory dimensions are latent bundles of correlated variables, and that it preserves interpretability by reconstructing those bundles. In the Gaussian simulations, mixed-SCGLR gives the most accurate fixed-effect estimates except at the lowest redundancy level; with Bernoulli and Poisson responses it outperforms GLMM-LASSO once redundancy is non-negligible ($\\tau > 0.3$). On a forest-ecology census of eight tree genera, accounting for within-concession random effects through mixed-SCGLR lowers cross-validation prediction error for every response relative to SCGLR. A sympathetic reader would care because many applied settings face both grouped outcomes and large sets of collinear proxies.","feed_headline":"Component method beats ridge and lasso on grouped data","feed_subtitle":"Mixed-SCGLR builds supervised components for multivariate GLMMs, cutting fixed-effect error as predictor redundancy rises.","key_machinery":"The load-bearing object is the mixed-SCGLR criterion $s\\log\\varphi(u) + (1-s)\\log\\psi_A(u)$, maximised over loading vectors $u$ under $u^T M^{-1} u = 1$ and, for higher-rank components, under orthogonality constraints. Here $\\psi_A(u)$ is the goodness-of-fit of component $f = Xu$ together with the additional variables $A$ for all responses, measured by weighted cosines between each response's Schall working variable and the spanned space with the response's weight matrix; $\\varphi(u)$ is the structural-relevance criterion, a weighted generalised average of squared correlations between $f$ and the original predictors, whose locality is tuned by $l$. This criterion is what makes the regularisation component-based rather than penalty-based: instead of shrinking coefficient norms, it pushes components toward interpretable bundles while preserving predictive fit. Schall's linearisation converts each conditional GLMM into a working linear mixed model, Henderson's equations update parameters and variance components, and the Projected Iterated Normed Gradient (PING) algorithm solves the constrained maximisation on the unit sphere.","core_discovery":"The paper establishes that the SCGLR supervised-component criterion, which trades goodness of fit against structural relevance of a component in the predictor space, can be transplanted into Schall's iterative linearisation of a GLMM. The algorithm alternates between computing a component $f = Xu$ that maximises the combined criterion on current working variables and weights, and solving Henderson mixed-model equations that update fixed effects, random-effect predictions, and variance components; the working variables and weights are then recomputed and the cycle repeats until stability. The reported simulations show that mixed-SCGLR recovers the predictive variable bundles on grouped data, even when a higher-inertia nuisance bundle is present, and that its fixed-effect estimates are the most accurate of the compared methods under strong within-bundle correlation. On the real data, mixed-SCGLR outperforms SCGLR on every response, showing that the random-effect term contributes to prediction rather than merely adjusting standard errors.","pith_inferences":["A natural next experiment is to replace only the parameter-estimation block of Algorithm 1 with a Laplace or MCMC fit while keeping the component-building step fixed; if component directions barely change, the component criterion is robust to the linearisation and the bias is concentrated in the variance components.","When responses are driven by disjoint rather than shared predictor bundles, the common-component formulation could inflate the number of components needed; a simulation with disjoint structures would quantify that cost.","The cross-validated locality parameter $l$ could itself be read as a diagnostic: small optimal $l$ indicates global principal-component-like structure, large $l$ indicates local bundles, so tuning doubles as an exploratory tool.","In the $p>n$ simulations the number of components kept is a stronger regularisation choice than in the low-dimensional case; varying $K$ jointly with the principal-component cutoff would reveal how much of the method's performance hinges on that choice."],"forward_implications":["With strongly redundant predictors arranged in bundles, component-based regularisation of a multivariate GLMM can give lower fixed-effect estimation error than ridge or LASSO, and the advantage grows with the within-bundle correlation $\\tau$.","Modelling within-group dependence is part of the predictive gain: on grouped data, mixed-SCGLR can beat non-mixed SCGLR for every response, as in the forest census.","Mixed-SCGLR yields interpretable output: component planes separate predictive bundles from high-inertia nuisance bundles, and the decomposition of each response's linear predictor onto common components reveals which responses share an explanatory dimension.","The same algorithm handles Gaussian, Bernoulli, binomial and Poisson responses, and its high-dimensional variant (using principal components of $X$) extends the approach to $p>n$ settings.","Because variance-component estimates from Schall's linearisation are biased toward zero for binary data, the paper anticipates that combined strategies, building components on the linearised model and estimating parameters by Monte Carlo methods, will be more reliable in that case."],"supporting_citations":[{"why":"Defines the SCGLR supervised-component criterion and its alternated Fisher-scoring estimation, which mixed-SCGLR extends to random effects.","marker":"Bry et al. (2013)"},{"why":"Refines SCGLR with the variable-powered inertia structural-relevance criterion and the $l$ locality tuning used throughout the simulations.","marker":"Bry et al. (2018)"},{"why":"Supplies the iterative linearisation of GLMMs into working linear mixed models that Algorithm 1 alternates with component computation.","marker":"Schall (1991)"},{"why":"Provides the mixed-model equations used to update fixed effects, random-effect predictions and variance components within each iteration.","marker":"Henderson (1975)"},{"why":"Gives the penalised-quasi-likelihood and Laplace approximation context that justifies the linearisation strategy for non-Gaussian GLMMs.","marker":"Breslow and Clayton (1993)"},{"why":"Defines the ridge-regularised linear mixed model that serves as a comparison baseline and supplies its generalised cross-validation calibration.","marker":"Eliot et al. (2011)"},{"why":"Defines the L1-penalised GLMM estimator used as the primary LASSO comparison in the simulations.","marker":"Groll and Tutz (2014)"},{"why":"Provides the GLMMLasso algorithm, the high-dimensional LASSO baseline against which mixed-SCGLR is compared.","marker":"Schelldorfer et al. (2014)"},{"why":"Introduces the LASSO estimator whose penalised approach is the main alternative regularisation compared in the simulations.","marker":"Tibshirani (1996)"},{"why":"Frames the joint-maximisation strategy that Schall's algorithm instantiates and documents the downward bias of variance-component estimates for binary GLMMs.","marker":"McCulloch (1997)"}],"fun_headline_variants":["Mixed-SCGLR regularises GLMMs, beats ridge and lasso","Component-based regularisation for GLMMs outperforms ridge, lasso","Supervised components improve multivariate GLMM prediction","Mixed-SCGLR: supervised components for grouped data","Extending SCGLR to GLMMs boosts predictive accuracy"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that Schall's linearisation, a penalised-quasi-likelihood-style approximation of the GLMM, is faithful enough that the working variables and weights still point toward the true latent explanatory dimensions; if the linearisation distorts the conditional model, the component directions, fixed-effect estimates, and variance-component updates can all be affected.","fun_headline_variants_meta":{"raw":{"variants":["Mixed-SCGLR regularises GLMMs, beats ridge and lasso","Component-based regularisation for GLMMs outperforms ridge, lasso","Supervised components improve multivariate GLMM prediction","Mixed-SCGLR: supervised components for grouped data","Extending SCGLR to GLMMs boosts predictive accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001078,"raw_usage":{"total_tokens":4485,"prompt_tokens":895,"completion_tokens":3590,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":511,"completion_tokens_details":{"reasoning_tokens":3503}},"tokens_in":511,"tokens_out":3590,"duration_ms":24110,"temperature":1.0,"reasoning_tokens":3503,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T13:53:51.361865+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Simulate grouped binary data from a known latent structure, fit the same data with mixed-SCGLR and with a GLMM estimated by adaptive Gauss-Hermite quadrature, and compare the first estimated component direction and the variance-component estimate across many replications; if the component direction shifts materially while the variance-component estimate is biased toward zero, Schall's linearisation is the approximation that needs replacing.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the SCGLR supervised-component criterion and its alternated Fisher-scoring estimation, which mixed-SCGLR extends to random effects."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Refines SCGLR with the variable-powered inertia structural-relevance criterion and the $l$ locality tuning used throughout the simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the iterative linearisation of GLMMs into working linear mixed models that Algorithm 1 alternates with component computation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the mixed-model equations used to update fixed effects, random-effect predictions and variance components within each iteration."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the penalised-quasi-likelihood and Laplace approximation context that justifies the linearisation strategy for non-Gaussian GLMMs."},{"cited_title":"P., and Foulkes, A","cited_arxiv_id":null,"evidence_quote":"Defines the ridge-regularised linear mixed model that serves as a comparison baseline and supplies its generalised cross-validation calibration."},{"cited_title":"and Tutz, G","cited_arxiv_id":null,"evidence_quote":"Defines the L1-penalised GLMM estimator used as the primary LASSO comparison in the simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the GLMMLasso algorithm, the high-dimensional LASSO baseline against which mixed-SCGLR is compared."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the LASSO estimator whose penalised approach is the main alternative regularisation compared in the simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Frames the joint-maximisation strategy that Schall's algorithm instantiates and documents the downward bias of variance-component estimates for binary GLMMs."}],"review_version":1}