Subgroup detection in linear growth curve models with generalized linear mixed model (GLMM) trees.

Growth curve models are popular tools for studying the development of a response variable within subjects over time. Heterogeneity between subjects is common in such models, and researchers are typically interested in explaining or predicting this heterogeneity. We show how generalized linear mixed-effects model (GLMM) trees can be used to identify subgroups with different trajectories in linear growth curve models. Originally developed for clustered cross-sectional data, GLMM trees are extended here to longitudinal data. The resulting extended GLMM trees are directly applicable to growth curve models as an important special case. In simulated and real-world data, we assess performance of the extensions and compare against other partitioning methods for growth curve models. Extended GLMM trees perform more accurately than the original algorithm and LongCART, and similarly accurate compared to structural equation model (SEM) trees. In addition, GLMM trees allow for modeling both discrete and continuous time series, are less sensitive to (mis-)specification of the random-effects structure and are much faster to compute.

An R toolbox for score-based measurement invariance tests in IRT models.

The detection of differential item functioning (DIF) is a central topic in psychometrics and educational measurement. In the past few years, a new family of score-based tests of measurement invariance has been proposed, which allows the detection of DIF along arbitrary person covariates in a variety of item response theory (IRT) models. This paper illustrates the application of these tests within the R system for statistical computing, making them accessible to a broad range of users. This presentation also includes IRT models for which these tests have not previously been investigated, such as the generalized partial credit model. The paper has three goals: First, we review the ideas behind score-based tests of measurement invariance. Second, we describe the implementation of these tests within the R system for statistical computing, which is based on the interaction of the R packages mirt, psychotools and strucchange. Third, we illustrate the application of this software and the interpretation of its output in two empirical datasets. The complete R code for reproducing our results is reported in the paper.

Motivation, values, and work design as drivers of participation in the R open source project for statistical computing.

One of the cornerstones of the R system for statistical computing is the multitude of packages contributed by numerous package authors. This amount of packages makes an extremely broad range of statistical techniques and other quantitative methods freely available. Thus far, no empirical study has investigated psychological factors that drive authors to participate in the R project. This article presents a study of R package authors, collecting data on different types of participation (number of packages, participation in mailing lists, participation in conferences), three psychological scales (types of motivation, psychological values, and work design characteristics), and various socio-demographic factors. The data are analyzed using item response models and subsequent generalized linear models, showing that the most important determinants for participation are a hybrid form of motivation and the social characteristics of the work design. Other factors are found to have less impact or influence only specific aspects of participation.

Using recursive partitioning to account for parameter heterogeneity in multinomial processing tree models.

In multinomial processing tree (MPT) models, individual differences between the participants in a study can lead to heterogeneity of the model parameters. While subject covariates may explain these differences, it is often unknown in advance how the parameters depend on the available covariates, that is, which variables play a role at all, interact, or have a nonlinear influence, etc. Therefore, a new approach for capturing parameter heterogeneity in MPT models is proposed based on the machine learning method MOB for model-based recursive partitioning. This procedure recursively partitions the covariate space, leading to an MPT tree with subgroups that are directly interpretable in terms of effects and interactions of the covariates. The pros and cons of MPT trees as a means of analyzing the effects of covariates in MPT model parameters are discussed based on simulation experiments as well as on two empirical applications from memory research. Software that implements MPT trees is provided via the mpttree function in the psychotree package in R.

Upper reference limits for cerebrospinal fluid total protein and albumin quotient based on a large cohort of control patients: implications for increased clinical specificity.

BACKGROUND: Determination of cerebrospinal fluid (CSF) total protein (TP) as well as of CSF/serum albumin quotient (Qalb) is part of the routine CSF work-up. However, currently used upper reference limits (URL) are not well validated leading to over-reporting of blood-CSF barrier dysfunction in approximately 15% of patients without neurological disease. The objective of this study was to determine age-related URL for CSF TP and Qalb in a cohort of control patients. METHODS: A total of 332 paired CSF and serum samples of patients without objective clinical and paraclinical findings of a neurological disease were analyzed for CSF TP and Qalb. CSF TP was measured by spectrophotometry and albumin in CSF and serum by nephelometry. RESULTS: CSF TP concentration and Qalb significantly correlated with age. In subjects at the age of 18-70 years, median CSF TP ranged from 320 to 460 mg/L and URL defined as the 95th percentile were 530-690 mg/L. Median Qalb ranged from 4.1 to 6.1 and URL from 8.7 up to 11.0. For URL of Qalb we calculated the following formula: age/25+8. CONCLUSIONS: Age-dependent URL for CSF TP and Qalb are presented here in a large cohort of control patients. They are higher than those currently recommended and this probably explains why isolated blood-CSF barrier dysfunction has been apparently over-reported. These new URL might be considered in a future revision of CSF guidelines.

Modeling Caries Experience: Advantages of the Use of the Hurdle Model.

In dental epidemiology, the decayed (D), missing (M), and filled (F) teeth or surfaces index (DFM index) is a frequently used measure. The DMF index is characterized by a strongly positive skewed distribution with a large stack of zero counts for those individuals without caries experience. Therefore, standard generalized linear models often lead to a poor fit. The hurdle regression model is a highly suitable class to model a DMF index, but its use is subordinated. We aim to overcome the gap between the suitability of the hurdle model to fit DMF indices and the frequency of its use in caries research. A theoretical introduction to the hurdle model is provided, and an extensive comparison with the zero-inflated model is given. Using an illustrative data example, both types of models are compared, with a special focus on interpretation of their parameters. Accompanying R code and example data are provided as online supplementary material.

Upward Lightning at Wind Turbines: Risk Assessment From Larger-Scale Meteorology.

Upward lightning (UL) has become a major threat to the growing number of wind turbines producing renewable electricity. It can be much more destructive than downward lightning due to the large charge transfer involved in the discharge process. Ground-truth lightning current measurements indicate that less than 50% of UL could be detected by lightning location systems (LLS). UL is expected to be the dominant lightning type during the cold season. However, current standards for assessing the risk of lightning at wind turbines mainly consider summer lightning, which is derived from LLS. This study assesses the risk of LLS-detectable and LLS-undetectable UL at wind turbines using direct UL measurements at instrumented towers. These are linked to meteorological data using random forests. The meteorological drivers for the absence/occurrence of UL are found from these models. In a second step, the results of the tower-trained models are extended to a larger study area (central and northern Germany). The tower-trained models for LLS-detectable lightning are independently verified at wind turbine sites in this area and found to reliably diagnose this type of UL. Risk maps based on cold season case study events show that high probabilities in the study area coincide with actual UL flashes. This lends credibility to the application of the model to all UL types, increasing both risk and affected areas.

Amplification of annual and diurnal cycles of alpine lightning.

The response of lightning to a changing climate is not fully understood. Historic trends of proxies known for fostering convective environments suggest an increase of lightning over large parts of Europe. Since lightning results from the interaction of processes on many scales, as many of these processes as possible must be considered for a comprehensive answer. Recent achievements of decade-long seamless lightning measurements and hourly reanalyses of atmospheric conditions including cloud micro-physics combined with flexible regression techniques have made a reliable reconstruction of cloud-to-ground lightning down to its seasonally varying diurnal cycle feasible. The European Eastern Alps and their surroundings are chosen as reconstruction region since this domain includes a large variety of land-cover, topographical and atmospheric circulation conditions. The most intense changes over the four decades from 1980 to 2019 occurred over the high Alps where lightning activity doubled in the 2010 s compared to the 1980 s. There, the lightning season reaches a higher maximum and starts one month earlier. Diurnally, the peak is up to 50% stronger with more lightning strikes in the afternoon and evening hours. Signals along the southern and northern alpine rim are similar but weaker whereas the flatlands surrounding the Alps have no significant trend.

Upward Lightning at the Gaisberg Tower: The Larger-Scale Meteorological Influence on the Triggering Mode and Flash Type.

Upward lightning is rarer than downward lightning and requires tall (100+ m) structures to initiate. It may be either self-initiated or triggered by other lightning discharges. While conventional lightning location systems (LLSs) detect most of the upward lightning flashes superimposed by pulses or return strokes, they miss a specific flash type that consists only of a continuous current. Globally, only few specially instrumented towers can record this flash type. The proliferation of wind turbines in combination with damages from upward lightning necessitates an improved understanding under which conditions self-initiated upward lightning and the continuous-current-only subtype occur. This study uses a random forest machine learning model to find the larger-scale meteorological conditions favoring the occurrence of the different phenomena. It combines ground truth lightning current measurements at the specially instrumented tower at Gaisberg mountain in Austria with variables from larger-scale meteorological reanalysis data (ERA5). These variables reliably explain whether upward lightning is self-initiated or triggered by other lightning discharges. The most important variable is the height of the -10°C isotherm above the tall structure: the closer it is, the higher is the probability of self-initiated upward lightning. For the different flash types, this study finds a relationship to the larger-scale electrification conditions and the LLS-detected lightning situation in the vicinity. Lower amounts of supercooled liquid water, solid, and liquid differently sized particles and no LLS-detected lightning events nearby favor the continuous-current-only subtype compared to the other subtypes, which preferentially occur with LLS-detected lightning events within 3 km from the Gaisberg Tower.

Anchor Point Selection: Scale Alignment Based on an Inequality Criterion.

For detecting differential item functioning (DIF) between two or more groups of test takers in the Rasch model, their item parameters need to be placed on the same scale. Typically this is done by means of choosing a set of so-called anchor items based on statistical tests or heuristics. Here the authors suggest an alternative strategy: By means of an inequality criterion from economics, the Gini Index, the item parameters are shifted to an optimal position where the item parameter estimates of the groups best overlap. Several toy examples, extensive simulation studies, and two empirical application examples are presented to illustrate the properties of the Gini Index as an anchor point selection criterion and compare its properties to those of the criterion used in the alignment approach of Asparouhov and Muthén. In particular, the authors show that-in addition to the globally optimal position for the anchor point-the criterion plot contains valuable additional information and may help discover unaccounted DIF-inducing multidimensionality. They further provide mathematical results that enable an efficient sparse grid optimization and make it feasible to extend the approach, for example, to multiple group scenarios.

Network Trees: A Method for Recursively Partitioning Covariance Structures.

In many areas of psychology, correlation-based network approaches (i.e., psychometric networks) have become a popular tool. In this paper, we propose an approach that recursively splits the sample based on covariates in order to detect significant differences in the structure of the covariance or correlation matrix. Psychometric networks or other correlation-based models (e.g., factor models) can be subsequently estimated from the resultant splits. We adapt model-based recursive partitioning and conditional inference tree approaches for finding covariate splits in a recursive manner. The empirical power of these approaches is studied in several simulation conditions. Examples are given using real-life data from personality and clinical research.

Conditional variable importance for random forests.

BACKGROUND: Random forests are becoming increasingly popular in many scientific fields because they can cope with "small n large p" problems, complex interactions and even highly correlated predictor variables. Their variable importance measures have recently been suggested as screening tools for, e.g., gene expression studies. However, these variable importance measures show a bias towards correlated predictor variables. RESULTS: We identify two mechanisms responsible for this finding: (i) A preference for the selection of correlated predictors in the tree building process and (ii) an additional advantage for correlated predictor variables induced by the unconditional permutation scheme that is employed in the computation of the variable importance measure. Based on these considerations we develop a new, conditional permutation scheme for the computation of the variable importance measure. CONCLUSION: The resulting conditional variable importance reflects the true impact of each predictor variable more reliably than the original marginal approach.

Generalized maximally selected statistics.

SUMMARY: Maximally selected statistics for the estimation of simple cutpoint models are embedded into a generalized conceptual framework based on conditional inference procedures. This powerful framework contains most of the published procedures in this area as special cases, such as maximally selected chi(2) and rank statistics, but also allows for direct construction of new test procedures for less standard test problems. As an application, a novel maximally selected rank statistic is derived from this framework for a censored response partitioned with respect to two ordered categorical covariates and potential interactions. This new test is employed to search for a high-risk group of rectal cancer patients treated with a neo-adjuvant chemoradiotherapy. Moreover, a new efficient algorithm for the evaluation of the asymptotic distribution for a large class of maximally selected statistics is given enabling the fast evaluation of a large number of cutpoints.

Individual treatment effect prediction for amyotrophic lateral sclerosis patients.

A treatment for a complicated disease might be helpful for some but not all patients, which makes predicting the treatment effect for new patients important yet challenging. Here we develop a method for predicting the treatment effect based on patient characteristics and use it for predicting the effect of the only drug (Riluzole) approved for treating amyotrophic lateral sclerosis. Our proposed method of model-based random forests detects similarities in the treatment effect among patients and on this basis computes personalised models for new patients. The entire procedure focuses on a base model, which usually contains the treatment indicator as a single covariate and takes the survival time or a health or treatment success measurement as primary outcome. This base model is used both to grow the model-based trees within the forest, in which the patient characteristics that interact with the treatment are split variables, and to compute the personalised models, in which the similarity measurements enter as weights. We applied the personalised models using data from several clinical trials for amyotrophic lateral sclerosis from the Pooled Resource Open-Access Clinical Trials database. Our results indicate that some amyotrophic lateral sclerosis patients benefit more from the drug Riluzole than others. Our method allows gradually shifting from stratified medicine to personalised medicine and can also be used in assessing the treatment effect for other diseases studied in a clinical trial.

Tree-Based Global Model Tests for Polytomous Rasch Models.

Psychometric measurement models are only valid if measurement invariance holds between test takers of different groups. Global model tests, such as the well-established likelihood ratio (LR) test, are sensitive to violations of measurement invariance, such as differential item functioning and differential step functioning. However, these traditional approaches are only applicable when comparing previously specified reference and focal groups, such as males and females. Here, we propose a new framework for global model tests for polytomous Rasch models based on a model-based recursive partitioning algorithm. With this approach, a priori specification of reference and focal groups is no longer necessary, because they are automatically detected in a data-driven way. The statistical background of the new framework is introduced along with an instructive example. A series of simulation studies illustrates and compares its statistical properties to the well-established LR test. While both the LR test and the new framework are sensitive to differential item functioning and differential step functioning and respect a given significance level regardless of true differences in the ability distributions, the new data-driven approach is more powerful when the group structure is not known a priori-as will usually be the case in practical applications. The usage and interpretation of the new method are illustrated in an empirical application example. A software implementation is freely available in the R system for statistical computing.

Score-Based Tests of Differential Item Functioning via Pairwise Maximum Likelihood Estimation.

Measurement invariance is a fundamental assumption in item response theory models, where the relationship between a latent construct (ability) and observed item responses is of interest. Violation of this assumption would render the scale misinterpreted or cause systematic bias against certain groups of persons. While a number of methods have been proposed to detect measurement invariance violations, they typically require advance definition of problematic item parameters and respondent grouping information. However, these pieces of information are typically unknown in practice. As an alternative, this paper focuses on a family of recently proposed tests based on stochastic processes of casewise derivatives of the likelihood function (i.e., scores). These score-based tests only require estimation of the null model (when measurement invariance is assumed to hold), and they have been previously applied in factor-analytic, continuous data contexts as well as in models of the Rasch family. In this paper, we aim to extend these tests to two-parameter item response models, with strong emphasis on pairwise maximum likelihood. The tests' theoretical background and implementation are detailed, and the tests' abilities to identify problematic item parameters are studied via simulation. An empirical example illustrating the tests' use in practice is also provided.

Bias in random forest variable importance measures: illustrations, sources and a solution.

BACKGROUND: Variable importance measures for random forests have been receiving increased attention as a means of variable selection in many classification tasks in bioinformatics and related scientific fields, for instance to select a subset of genetic markers relevant for the prediction of a certain disease. We show that random forest variable importance measures are a sensible means for variable selection in many applications, but are not reliable in situations where potential predictor variables vary in their scale of measurement or their number of categories. This is particularly important in genomics and computational biology, where predictors often include variables of different types, for example when predictors include both sequence data and continuous variables such as folding energy, or when amino acid sequence data show different numbers of categories. RESULTS: Simulation studies are presented illustrating that, when random forest variable importance measures are used with data of varying types, the results are misleading because suboptimal predictor variables may be artificially preferred in variable selection. The two mechanisms underlying this deficiency are biased variable selection in the individual classification trees used to build the random forest on one hand, and effects induced by bootstrap sampling with replacement on the other hand. CONCLUSION: We propose to employ an alternative implementation of random forests, that provides unbiased variable selection in the individual classification trees. When this method is applied using subsampling without replacement, the resulting variable importance measures can be used reliably for variable selection even in situations where the potential predictor variables vary in their scale of measurement or their number of categories. The usage of both random forest algorithms and their variable importance measures in the R system for statistical computing is illustrated and documented thoroughly in an application re-analyzing data from a study on RNA editing. Therefore the suggested method can be applied straightforwardly by scientists in bioinformatics research.

Spatio-temporal precipitation climatology over complex terrain using a censored additive regression model.

Flexible spatio-temporal models are widely used to create reliable and accurate estimates for precipitation climatologies. Most models are based on square root transformed monthly or annual means, where a normal distribution seems to be appropriate. This assumption becomes invalid on a daily time scale as the observations involve large fractions of zero observations and are limited to non-negative values. We develop a novel spatio-temporal model to estimate the full climatological distribution of precipitation on a daily time scale over complex terrain using a left-censored normal distribution. The results demonstrate that the new method is able to account for the non-normal distribution and the large fraction of zero observations. The new climatology provides the full climatological distribution on a very high spatial and temporal resolution, and is competitive with, or even outperforms existing methods, even for arbitrary locations.

The impact of interventions on a pre-industrial Austrian Alpine population.

The purpose of the present study is to gain a better understanding of the role of culture in demographic behaviour. The case study uses demographic data to illustrate cultural factors intervening in the social organisation of an Austrian village in the period 1700-1900. Two sets of potential intervening variables that might explain the effects of culture on demographic behaviour were investigated: population policies through normative regulations and institutional changes due to shifts in government. The paper employs statistical techniques in a structural change setting for evaluating the impact of policies and institutional changes on the demographic development. There is clear evidence that normative interventions concerning the fraction of illegitimate births and the marriage pattern were effective.

Model-Based Recursive Partitioning for Subgroup Analyses.

The identification of patient subgroups with differential treatment effects is the first step towards individualised treatments. A current draft guideline by the EMA discusses potentials and problems in subgroup analyses and formulated challenges to the development of appropriate statistical procedures for the data-driven identification of patient subgroups. We introduce model-based recursive partitioning as a procedure for the automated detection of patient subgroups that are identifiable by predictive factors. The method starts with a model for the overall treatment effect as defined for the primary analysis in the study protocol and uses measures for detecting parameter instabilities in this treatment effect. The procedure produces a segmented model with differential treatment parameters corresponding to each patient subgroup. The subgroups are linked to predictive factors by means of a decision tree. The method is applied to the search for subgroups of patients suffering from amyotrophic lateral sclerosis that differ with respect to their Riluzole treatment effect, the only currently approved drug for this disease.