Nodes Of Tree Research Articles

Expectile regression forest: A new nonparametric expectile regression model

AbstractClassical nonlinear expectile regression has two shortcomings. It is difficult to choose a nonlinear function, and it does not consider the interaction effects among explanatory variables. Therefore, we combine the random forest model with the expectile regression method to propose a new nonparametric expectile regression model: expectile regression forest (ERF). The major novelty of the ERF model is using the bagging method to build multiple decision trees, calculating the conditional expectile of each leaf node in each decision tree, and deriving final results through aggregating these decision tree results via simple average approach. At the same time, in order to compensate for the black box problem in the model interpretation of the ERF model, the measurement of the importance of explanatory variable and the partial dependence is defined to evaluate the magnitude and direction of the influence of each explanatory variable on the response variable. The advantage of ERF model is illustrated by Monte Carlo simulation studies. The numerical simulation results show that the estimation and prediction ability of the ERF model is significantly better than alternative approaches. We also apply the ERF model to analyse the real data. From the nonparametric expectile regression analysis of these data sets, we have several conclusions that are consistent with the results of numerical simulation.

Multitree Search for Multisatellite Responsiveness Scheduling Considering Orbital Maneuvering

Rapid and responsive earth observation satellites enable the evaluation of disaster risk, improve relief effectiveness, and reduce suffering and fatalities in the event of sudden disaster events.One promising method for responsive space satellites is orbital maneuvering. This paper describes a multi-tree search framework for multi-satellite responsiveness scheduling considering orbital maneuvering, where multiple ground targets are cooperatively observed by multiple observation satellites over a short period of time. Based on the traditional tree search, the proposed method constructs multiple trees and distributes all the targets to multiple satellites, allowing the observation sequence of single satellite to be optimized. To apply the tree search algorithm, a tree node collection (TNC) composed of the corresponding nodes in multiple trees is used to represent the state of each satellite. Before the expansion phase, one specific node in the TNC is determined for later expansion. A beam search is then used to optimize the observation sequence. Ground track adjustment techniques using impulse maneuver are considered for visiting a given target. The proposed framework achieves better performance than the previous best method in a typical multi-satellite responsiveness scheduling problem scenario.

Enhancing Weak Nodes in Decision Tree Algorithm Using Data Augmentation

Abstract Decision trees are among the most popular classifiers in machine learning, artificial intelligence, and pattern recognition because they are accurate and easy to interpret. During the tree construction, a node containing too few observations (weak node) could still get split, and then the resulted split is unreliable and statistically has no value. Many existing machine-learning methods can resolve this issue, such as pruning, which removes the tree’s non-meaningful parts. This paper deals with the weak nodes differently; we introduce a new algorithm Enhancing Weak Nodes in Decision Tree (EWNDT), which reinforces them by increasing their data from other similar tree nodes. We called the data augmentation a virtual merging because we temporarily recalculate the best splitting attribute and the best threshold in the weak node. We have used two approaches to defining the similarity between two nodes. The experimental results are verified using benchmark datasets from the UCI machine-learning repository. The results indicate that the EWNDT algorithm gives a good performance.

Authenticity Verification for Dynamic Social Data Outsourcing

As with the maturation and diversification of social services, social data outsourcing has become pervasive. In this context, online social networks outsource their real-time social data to a social data provider, who responses to query requests issued from data consumers. However, dishonest or malicious social data providers might tamper with collected social data by adding fake data and deleting/modifying raw data, and further return inauthentic query results to data consumers. In this article, we make the first attempt to study the problem of authenticity verification for dynamic social data. To this end, we first propose a novel authenticity verification framework, and then, propose a self-balancing hash tree scheme to tackle challenges brought on by the vast scale and dynamics of social data. To maximize the search efficiency for the self-balancing hash tree, we introduce a balance factor to define an unbalanced node as its balance factor is not chosen from a predetermined set. Furthermore, we propose three algorithms to balance unbalanced nodes in the self-balancing hash tree. Rigorous theoretical analyses prove that our framework can determinately detect any fake query results returned by data consumers. Experimental results built on a real Twitter dataset show that our scheme is efficient and effective.

Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

Partial differential equations (PDEs) are concise and understandable representations of domain knowledge, which are essential for deepening our understanding of physical processes and predicting future responses. However, the PDEs of many real-world problems are uncertain, which calls for PDE discovery. We propose the symbolic genetic algorithm (SGA-PDE) to discover open-form PDEs directly from data without prior knowledge about the equation structure. SGA-PDE focuses on the representation and optimization of PDE. Firstly, SGA-PDE uses symbolic mathematics to realize the flexible representation of any given PDE, transforms a PDE into a forest, and converts each function term into a binary tree. Secondly, SGA-PDE adopts a specially designed genetic algorithm to efficiently optimize the binary trees by iteratively updating the tree topology and node attributes. The SGA-PDE is gradient-free, which is a desirable characteristic in PDE discovery since it is difficult to obtain the gradient between the PDE loss and the PDE structure. In the experiment, SGA-PDE not only successfully discovered nonlinear Burgers' equation, Korteweg-de Vries (KdV) equation, and Chafee-Infante equation, but also handled PDEs with fractional structure and compound functions that cannot be solved by conventional PDE discovery methods.

The traversal method for user address space in Windows 10 system based on VAD tree

The existing traversal method for user address space in the memory forensic research is only applicable to Windows XP and Windows 7 32-bit system. Windows 10 64-bit system is currently used by most users, which is the main target of network attackers. A method to traverse Windows 10 user address space based on VAD(virtual address descriptor) tree is proposed. The memory kernel and user address space metadata of Windows 10 64-bit system was located. The related metadata such as mapping files, shared memory, heap, stack and reserved system structures were parsed and matched with the information in VAD tree nodes. The starting address, ending address, used size, allocating protection, memory type and details of each memory area were output. The results show that the method is compatible with all versions of Windows 10 64-bit system and can effectively traverse common structures when dealing with processes with different complexity.

A decision tree-assisted polynomial regression model with application in the cutting force analysis of cutters of a tunnel boring machine

Polynomial regression (PR) has been widely used to model simulations and experimental engineering data. The regression relationship of engineering data often varies greatly in different sub-sample spaces, making it difficult to evaluate accurately using a unified PR model. To solve this issue, a decision tree-assisted polynomial regression (DTPR) model is proposed in this article, in which a new decision tree is designed to partition the sample space according to the regression relationship. To make a prediction for a new sample, it is first compared from the root node of the decision tree until it reaches a leaf node; then, the output is obtained through the PR model of the leaf node. The experimental results indicate that the proposed model can show competitive performance in both mathematical functions and engineering cases. The proposed model is applied to the cutting force analysis of cutters of a tunnel boring machine to demonstrate its advantages.

PHACT: Phylogeny-Aware Computing of Tolerance for Missense Mutations.

Evolutionary conservation is a fundamental resource for predicting the substitutability of amino acids and the loss of function in proteins. The use of multiple sequence alignment alone—without considering the evolutionary relationships among sequences—results in the redundant counting of evolutionarily related alteration events, as if they were independent. Here, we propose a new method, PHACT, that predicts the pathogenicity of missense mutations directly from the phylogenetic tree of proteins. PHACT travels through the nodes of the phylogenetic tree and evaluates the deleteriousness of a substitution based on the probability differences of ancestral amino acids between neighboring nodes in the tree. Moreover, PHACT assigns weights to each node in the tree based on their distance to the query organism. For each potential amino acid substitution, the algorithm generates a score that is used to calculate the effect of substitution on protein function. To analyze the predictive performance of PHACT, we performed various experiments over the subsets of two datasets that include 3,023 proteins and 61,662 variants in total. The experiments demonstrated that our method outperformed the widely used pathogenicity prediction tools (i.e., SIFT and PolyPhen-2) and achieved a better predictive performance than other conventional statistical approaches presented in dbNSFP. The PHACT source code is available at https://github.com/CompGenomeLab/PHACT.

Clinical analysis and artificial intelligence survival prediction of serous ovarian cancer based on preoperative circulating leukocytes

Circulating leukocytes are an important part of the immune system. The aim of this work is to explore the role of preoperative circulating leukocytes in serous ovarian carcinoma and investigate whether they can be used to predict survival prognosis. Routine blood test results and clinical information of patients with serous ovarian carcinoma were retrospectively collected. And to predict survival according to the blood routine test result the decision tree method was applied to build a machine learning model.The results showed that the number of preoperative white blood cells (p = 0.022), monocytes (p < 0.001), lymphocytes (p < 0.001), neutrophils (p < 0.001), and eosinophils (p < 0.001) and the monocyte to lymphocyte (MO/LY) ratio in the serous ovarian cancer group were significantly different from those in the control group. These factors also showed a correlation with other clinicopathological characteristics. The MO/LY was the root node of the decision tree, and the predictive AUC for survival was 0.69. The features involved in the decision tree were the MO/LY, differentiation status, CA125 level, neutrophils (NE,) ascites cytology, LY% and age.In conclusion, the number and percentage of preoperative leukocytes in patients with ovarian cancer is changed significantly compared to those in the normal control group, as well as the MO/LY. A decision tree was built to predict the survival of patients with serous ovarian cancer based on the CA125 level, white blood cell (WBC) count, presence of lymph node metastasis (LNM), MO count, the MO/LY ratio, differentiation status, stage, LY%, ascites cytology, and age.

Spatial Concept Query Based on Lattice-Tree

As a basic method of spatial data operation, spatial keyword query can provide meaningful information to meet user demands by searching spatial textual datasets. How to accurately understand users’ intentions and efficiently retrieve results from spatial textual big data are always the focus of research. Spatial textual big data and their complex correlation between textual features not only enrich the connotation of spatial objects but also bring difficulties to the efficient recognition and retrieval of similar spatial objects. Because there are a lot of many-to-many relationships between massive spatial objects and textual features, most of the existing research results that employ tree-like and table-like structures to index spatial data and textual data are inefficient in retrieving similar spatial objects. In this paper, firstly, we define spatial textual concept (STC) as a group of spatial objects with the same textual keywords in a limited spatial region in order to present the many-to-many relationships between spatial objects and textual features. Then we attempt to introduce the concept lattice model to maintain a group of related STCs and propose a hybrid tree-like spatial index structure, the lattice-tree, for spatial textual big data. Lattice-tree employs R-tree to index the spatial location of objects, and it embeds a concept lattice structure into specific tree nodes to organize the STC set from a large number of textual keywords of objects and their relationships. Based on this, we also propose a novel spatial keyword query, named Top-k spatial concept query (TkSCQ), to answer STC and retrieve similar spatial objects with multiple textual features. The empirical study is carried out on two spatial textual big data sets from Yelp and Amap. Experiments on the lattice-tree verify its feasibility and demonstrate that it is efficient to embed the concept lattice structure into tree nodes of 3 to 5 levels. Experiments on TkSCQ evaluate lattice from results, keywords, data volume, and so on, and two baseline index structures based on IR-tree and Fp-tree, named the inverted-tree and Fpindex-tree, are developed to compare with the lattice-tree on data sets from Yelp and Amap. Experimental results demonstrate that the Lattice-tree has the better retrieval efficiency in most cases, especially in the case of large amounts of data queries, where the retrieval performance of the lattice-tree is much better than the inverted-tree and Fpindex-tree.

A tree search heuristic for the resource constrained project scheduling problem with transfer times

In this work, we study the resource constrained project scheduling problem with transfer times, where the transfer of resources between activities takes a certain amount of time. For the problem, we propose an improved serial schedule generation scheme, a new lower bound, and a tree search heuristic. To generate a schedule, the improved serial schedule generation scheme iteratively schedules an activity by breaking some existing resource flows and decides the earliest start time in an efficient way. The new lower bound is adapted from the critical capacity lower bound by additionally considering resource transfer times. The tree search heuristic utilizes the improved serial schedule generation scheme to schedule an activity at its earliest start time and the new lower bound to prune unpromising nodes in the search tree. Several priority rules are introduced in the heuristic for the selection of the next activity during branching and also used in a greedy algorithm to compute an upper bound for node evaluation. Computational experiments on benchmark instances show that the improved serial schedule generation scheme reduces the computational time by 91.30% on average compared to an existing serial schedule generation scheme from literature, the new lower bound dominates the known adapted critical path lower bound and achieves an average improvement of 7.95%, and the tree search heuristic performs better than three existing algorithms for the problem.

Toward Optimally Efficient Search With Deep Learning for Large-Scale MIMO Systems

This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the decision tree. Unfortunately, the existing optimal search algorithms often involve prohibitively high complexities, which indicates that they are infeasible in large-scale MIMO systems. To address this issue, we propose a general heuristic search algorithm, namely, hyper-accelerated tree search (HATS) algorithm. The proposed algorithm employs a deep neural network (DNN) to estimate the optimal heuristic, and then use the estimated heuristic to speed up the underlying memory-bounded search algorithm. This idea is inspired by the fact that the underlying heuristic search algorithm reaches the optimal efficiency with the optimal heuristic function. Simulation results show that the proposed algorithm reaches almost the optimal bit error rate (BER) performance in large-scale systems, while the memory size can be bounded. In the meanwhile, it visits nearly the fewest tree nodes. This indicates that the proposed algorithm reaches almost the optimal efficiency in practical scenarios, and thereby it is applicable for large-scale systems. Besides, the code for this paper is available at \url{https://github.com/skypitcher/hats}.

A branch-and-price approach to a variant of the cognitive radio resource allocation problem

Radio-frequency portion of the electromagnetic spectrum is a scarce resource. Cognitive radio (CR) technology has emerged as a promising solution to overcome the spectrum scarcity bottleneck. Through this technology, secondary users (SUs) sense the spectrum opportunities free from primary users (PUs), and opportunistically take advantage of these (temporarily) idle portions, known as spectrum holes. In this correspondence, we consider a variant of the cognitive radio resource allocation problem posed by Martinovic et al. in 2017. The distinguishing feature of this version of the problem is that each SU, due to its hardware limitations, imposes the requirement that the to-be-aggregated spectrum holes cannot be arbitrarily far from each other. We call this restriction as the Maximal Aggregation Range (MAR) constraint, and refer to this variant of the problem as the MAR-constrained hole assignment problem. The problem can be formalized as an NP-hard combinatorial optimization problem. We propose a novel binary integer linear programming (ILP) formulation to the problem. The number of constraints in this formulation is the number of spectrum holes plus the number of SUs. On the other hand, the number of binary decision variables in the formulation can be prohibitively large, as for each legitimate spectrum allocation to each SU, one variable is needed. Due to this difficulty, the resulting 0-1 ILP instances may not even be explicitly describable, let alone be solvable by an ILP solver. We propose a branch-and-price (B&P) framework to tackle this challenge. This framework is in fact a branch-and-bound procedure in which at each node of the search tree, we utilize the so-called (delayed) column generation technique for solving the LP relaxation of the corresponding subproblem. As evidenced by the numerical results, the LP relaxation bounds are very tight. This allows for a very effective pruning of the search space. Compared to the previously suggested formulations, the proposed technique can require much less computational effort.

Recurrent evolutionary changes in pollen shape and ornamentation of the vataireoid clade (Papilionoideae, Fabaceae), an early-branching lineage of florally divergent genera

Abstract Pollen traits have clarified the classification and understanding of the evolutionary history of different groups of angiosperms, due to their wide morphological diversity. To increase our knowledge on the morphological evolution of the vataireoid clade (Fabaceae, Papilionoideae), a lineage comprising 30 species of Neotropical trees in the genera Luetzelburgia, Sweetia, Vatairea and Vataireopsis, pollen materials of 26 species were acetolysed and analysed using light and scanning electron microscopy. Characters were defined to reconstruct the pollen evolution in each of the ancestral nodes of the phylogenetic tree of the clade using Bayesian stochastic character mapping. All vataireoid genera have relatively variable pollen morphology, ranging from small to medium and subtriangular to circular amb, and their aperture margo may be present or absent. The exine ornamentation varies greatly across the clade: perforate (L. praecox and S. fruticosa); rugulate (L. andradelimae); rugulate-foveolate-perforate (Vatairea guianensis and Vatairea heteroptera); reticulate (Vataireopsis araroba) and microreticulate in most species. Analyses of ancestral character reconstruction revealed multiple events of independent evolution in all pollen traits during the diversification of the vataireoid clade in the last 16 Myr, since the Miocene. Just as evolutionary transitions in floral architecture were so recurrent in the vataireoid clade, pollen evolution was relatively labile and exhibited little phylogenetic conservatism in shape or ornamentation.

Clinical Variables in Predicting Survival and Hospitalization for Pulmonary Arterial Hypertension Using Harmonized Data

<h3>Purpose</h3> Pulmonary arterial hypertension (PAH) is a type of high blood pressure that affects arteries in the lungs and the heart. Although clinical trials have been actively conducted, data from different trials are seldom harmonized for a more powerful study. In this study, we built a repository of harmonized data for adult PAH research. We then used the harmonized data to analyze clinical variables in predicting survival, and we also demonstrated the potential utility of the data for predicting hospitalization. <h3>Methods</h3> We cleaned data from seven adult PAH trials: GRIPHON, SERAPHIN, EARLY, COMPASS-2, COMPASS-3, MAESTRO and TRANSIT-1. Data from separate studies were merged as one harmonized data set. Using the harmonized data, we conducted Cox proportional hazard analysis to study the association between time to death at 30 days and each of two variables obtained at baseline, pulmonary artery pulsatility index (PAPi) and aortic pulsatility index (API). Using data from the GRIPHON study, we also constructed a Bayesian network to predict the outcome of hospitalization from clinical variables. The Tree-Augmented naive Bayes algorithm was implemented. The cutoff values discretizing continuous variables were obtained using a classification tree. <h3>Results</h3> The harmonized data comprise 2,870 subjects and 178 variables, with rich information including demographic, laboratory, electrocardiogram, vital sign, right heart catheterization, echocardiography, hospitalization and mortality. In our analysis, PAPi was shown to be significantly associated with time to death at 30 days. The p-value was 0.010 and the hazard ratio was 0.838 with a 95% confidence interval being (0.734, 0.958). The top three nodes of the classification tree were bilirubin less than 0.50 mg/dl, blood urea nitrogen less than 30.10 mg/dl, and WHO functional class II. Using the GRIPHON study as an example, the Bayesian network showed bilirubin, the top variable selected by the classification tree, was correlated with NP-proBNP, a well-known biomarker for evaluating the severity of heart disease. <h3>Conclusion</h3> The harmonized data is a valuable resource for PAH research. Our results suggest that PAPi may be an important biomarker for predicting survival. Additional biomarkers may also be minded from the harmonized data for other outcomes of interest, including hospitalization.

A Dynamic Cache Allocation Mechanism (DCAM) for Reliable Multicast in Information-Centric Networking

As a new network architecture, information-centric networking (ICN) decouples the identifiers and locators of network entities and makes full use of in-network cache technology to improve the content distribution efficiency. For reliable multicast, ICN in-network cache can help reduce the loss recovery delay. However, with the development of applications and services, a multicast tree node often serves multiple reliable multicast groups. How to reasonably allocate cache resources for each multicast group will greatly affect the performance of reliable multicast. In order to improve the overall loss recovery performance of reliable multicast, this paper designs a dynamic cache allocation mechanism (DCAM). DCAM considers the packet loss probability, the node depth of the multicast tree, and the multicast transmission rate of multicast group, and then allocates cache space for multicast group based on the normalized cache quota weight. We also explore the performance of three cache allocation mechanisms (DCAM, AARM, and Equal) combined with four cache strategies (LCE, CAPC, Prob, and ProbCache), respectively. Experimental results show that DCAM can adjust cache allocation results in time according to network changes, and its combinations with various cache strategies outperform other combinations. Moreover, the combination of DCAM and CAPC can achieve optimal performance in loss recovery delay, cache hit ratio, transmission completion time, and overhead.

Real-Time Directed Rapidly Exploring Random Tree Path Planning for Air Collision Avoidance

In this paper, a path planning algorithm is proposed for dynamic obstacle avoidance by improving a rapidly exploring random tree (RRT) algorithm, a sampling-based path-planning algorithm. Although guaranteeing a globally optimal path is impossible when using RRT algorithm, it is advantageous because it can generate the path quickly. Considering this advantage of the RRT algorithm, the directed RRT (DRRT) algorithm was developed, which reduces the generation time and supplements optimality by improving node generation and tree expansion process. It is also added the path smoothing method for the flight. The anytime DRRT algorithm is based on the DRRT algorithm and repeats path generation within the time limit considering the direction of movement of the obstacle and selects the shortest path for the flight. Air collision avoidance between unmanned aerial vehicles (UAVs) considering the intruders as a dynamic obstacle was simulated using the Gazebo simulator. Based on the simulation, the performance of the proposed anytime DRRT algorithm was verified with varying the host UAV and intruder conditions, and its applicability to UAVs was affirmed.

Obstacle avoidance path scheme of snake robot based on bidirectional fast expanding random tree algorithm

With the continuous innovation and development of related technologies in the field of robotics, various robots have emerged in large numbers, the application scenarios of robots are becoming more and more complex, and the requirements for robot technology are also getting higher and higher. As an indispensable part of robotics research, path planning technology has very important research and application value. As a new movable snake-shaped robot, the snake-shaped robot has always been a research hotspot in the field of snake-shaped robots due to its multi-gait movement ability and strong environmental adaptability. Among the various motion forms of the snake-shaped robot, the winding motion has the highest efficiency, and the snake-shaped robot in this motion form can also assist itself in its movement by contact with obstacles. However, there are few researches on the obstacle-assisted motion of snake-like robots, and the algorithm for solving collision dynamics is relatively simple. Therefore, it is necessary to conduct in-depth research on obstacle-assisted motion snake-like robots. The trajectory planning algorithm of the multi-NAO snake robot is studied. First, it analyzes the basic principles and implementation steps of the RRT algorithm and evaluates its advantages and disadvantages. On this basis, an improved fast-expanding random algorithm is proposed for the shortcomings of the RRT algorithm. Combining the advantages of the global search of the RRT algorithm, it is necessary to introduce an appropriate local search algorithm. Under the premise of ensuring that the path can be generated, a certain algorithm is added to improve the smoothness of the path, in order to reduce the turning time of the snake-like robot when it walks, and improve the search efficiency. Aiming at the randomness of RRT when generating random tree nodes, other algorithms are purposefully introduced to enable it to grow toward the target point. Path planning simulations verify that the improved two-way rapid expansion random tree algorithm has significantly improved search speed and search efficiency compared with Basic-RRT and Bi-RRT algorithms, with shorter average planning time and higher success rate, the generated path is smoother. Improved algorithm can not only avoid static global obstacles in a dynamic environment, but also efficiently avoid sudden dynamic obstacles. The real-time dynamic obstacle avoidance experiments based on the FANUC snake-shaped robot guiding the anthropomorphic obstacles to move and rotate in translation and the snake-shaped robot dynamically avoiding real human arms verify that the proposed algorithm can dynamically avoid regular and irregular moving obstacles online in time. When the number of obstacles is 3, the number of successful plans is 49, and the planning time is 55 ms; when the number of obstacles is 12, the number of successful plans is 40, and the planning time is 88.9 ms. Obviously, the increase in the number of obstacles leads to a decrease in the number of successful planning and an increase in planning time.

Performance Enhancement of Tree-based Friends-of-friends Galaxy Finder for High-resolution Simulations of Galaxy Formation

Abstract Cosmological simulations are useful tools for studying the evolution of galaxies, and it is critical to accurately identify galaxies and their halos from raw simulation data. The friends-of-friends (FoF) algorithm has been widely adopted for this purpose because of its simplicity and expandability to higher dimensions. However, it is cost-inefficient when applied to high-resolution simulations because standard FoF implementation leads to too many distance calculations in dense regions. We confirm this through our exercise of applying the six-dimensional (6D) FoF galaxy finder code, VELOCIraptor, on the NewHorizon simulation. The high particle resolution of NewHorizon (M star ∼ 104 M ⊙) allows a large central number density (106 kpc−3) for typical galaxies, resulting in a few days to weeks of galaxy searches for just one snapshot. Even worse, we observed a significant decrease in the FoF performance in the high-dimensional 6D searches: “the curse of dimensionality” problem. To overcome these issues, we have developed several implementations that can be readily applied to any tree-based FoF code. They include limiting visits to tree nodes, reordering the list of particles for searching neighbor particles, and altering the tree structure. Compared to the run with the original code, the new run with these implementations results in the identical galaxy detection with the ideal performance, O ( N log N ) , N being the number of particles in a galaxy—with a speed gain of a factor of 2700 in 3D or 12 in a 6D FoF search.

A New Stopping Criterion for Rasch Trees Based on the Mantel-Haenszel Effect Size Measure for Differential Item Functioning.

To detect differential item functioning (DIF), Rasch trees search for optimal splitpoints in covariates and identify subgroups of respondents in a data-driven way. To determine whether and in which covariate a split should be performed, Rasch trees use statistical significance tests. Consequently, Rasch trees are more likely to label small DIF effects as significant in larger samples. This leads to larger trees, which split the sample into more subgroups. What would be more desirable is an approach that is driven more by effect size rather than sample size. In order to achieve this, we suggest to implement an additional stopping criterion: the popular Educational Testing Service (ETS) classification scheme based on the Mantel-Haenszel odds ratio. This criterion helps us to evaluate whether a split in a Rasch tree is based on a substantial or an ignorable difference in item parameters, and it allows the Rasch tree to stop growing when DIF between the identified subgroups is small. Furthermore, it supports identifying DIF items and quantifying DIF effect sizes in each split. Based on simulation results, we conclude that the Mantel-Haenszel effect size further reduces unnecessary splits in Rasch trees under the null hypothesis, or when the sample size is large but DIF effects are negligible. To make the stopping criterion easy-to-use for applied researchers, we have implemented the procedure in the statistical software R. Finally, we discuss how DIF effects between different nodes in a Rasch tree can be interpreted and emphasize the importance of purification strategies for the Mantel-Haenszel procedure on tree stopping and DIF item classification.