Investigating Local Dependence With Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129-151 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Kernel Smoothing ◽  
Item Difficulty ◽  
Estimation Procedure ◽  
Local Dependence ◽  
Function Estimation ◽  
Conditional Covariance ◽  
Monotonic Transformation ◽  
Covariance Functions ◽  
Latent Space ◽  
Latent Ability

The local dependence of item pairs is investigated via a conditional covariance function estimation procedure. The conditioning variable used in the procedure is obtained by a monotonic transformation of total score on the remaining items. Intuitively, the conditioning variable corresponds to the unidimensional latent ability that is best measured by the test. The conditional covariance functions are estimated using kernel smoothing, and a standardization to adjust for the confounding effect of item difficulty is introduced. The particular standardization chosen is an adaptation of Yule’s coefficient of colligation. Several models of local dependence are discussed to explain special situations, such as speededness and latent space multidimensionality, in which the assumptions of unidimensionality and local independence are violated.

Investigating Local Dependence with Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Local Dependence ◽  
Conditional Covariance ◽  
Covariance Functions

scholarly journals A Generic Approach to Covariance Function Estimation Using ARMA-Models

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 591 ◽  
Author(s):  
Till Schubert ◽  
Johannes Korte ◽  
Jan Martin Brockmann ◽  
Wolf-Dieter Schuh
Keyword(s):  
Numerical Method ◽  
Covariance Function ◽  
Function Estimation ◽  
Arma Models ◽  
Linear System Of Equations ◽  
Covariance Functions ◽  
Analytical Functions ◽  
Covariance Modeling ◽  
Base Functions ◽  
Finite Sum

Covariance function modeling is an essential part of stochastic methodology. Many processes in geodetic applications have rather complex, often oscillating covariance functions, where it is difficult to find corresponding analytical functions for modeling. This paper aims to give the methodological foundations for an advanced covariance modeling and elaborates a set of generic base functions which can be used for flexible covariance modeling. In particular, we provide a straightforward procedure and guidelines for a generic approach to the fitting of oscillating covariance functions to an empirical sequence of covariances. The underlying methodology is developed based on the well known properties of autoregressive processes in time series. The surprising simplicity of the proposed covariance model is that it corresponds to a finite sum of covariance functions of second-order Gauss–Markov (SOGM) processes. Furthermore, the great benefit is that the method is automated to a great extent and directly results in the appropriate model. A manual decision for a set of components is not required. Notably, the numerical method can be easily extended to ARMA-processes, which results in the same linear system of equations. Although the underlying mathematical methodology is extensively complex, the results can be obtained from a simple and straightforward numerical method.

scholarly journals Smoothed Conditional Scale Function Estimation in AR(1)-ARCH(1) Processes

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Lema Logamou Seknewna ◽  
Peter Mwita Nyamuhanga ◽  
Benjamin Kyalo Muema
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Kernel Smoothing ◽  
Asymptotic Properties ◽  
Scale Function ◽  
Function Estimation

The estimation of the Smoothed Conditional Scale Function for time series was taken out under the conditional heteroscedastic innovations by imitating the kernel smoothing in nonparametric QAR-QARCH scheme. The estimation was taken out based on the quantile regression methodology proposed by Koenker and Bassett. And the proof of the asymptotic properties of the Conditional Scale Function estimator for this type of process was given and its consistency was shown.

A Kernel-Smoothed Version of SIBTEST With Applications to Local DIF Inference and Function Estimation

1996 ◽  
Vol 21 (4) ◽  
pp. 333-363 ◽  
Author(s):  
Jeffrey A. Douglas ◽  
William Stout ◽  
Louis V. DiBello
Keyword(s):  
Data Analysis ◽  
Item Response ◽  
Kernel Smoothing ◽  
Latent Trait ◽  
Real Data ◽  
Estimation Bias ◽  
Function Estimation ◽  
Item Response Function ◽  
And Function ◽  
Response Function Estimation

Smoothed SIBTEST, a nonparametric DIF detection procedure, amalgamates SIBTEST and kernel-smoothed item response function estimation. This procedure assesses DIF as a function of the latent trait θ that the test is designed to measure. Smoothed SIBTEST estimates this Junction with increased efficiency, as compared to SIBTEST, while providing hypothesis tests of local and global DIF. By means of kernel smoothing, smoothed SIBTEST reduces noise in local DIF estimation while retaining SIBTEST’s reduction of group-ability-difference-induced DIF estimation bias via use of regression-corrected estimates of ability as design points in the kernel smoothing. By contrast with most nonparametric procedures, matched examinee score cells are not needed, so sparse cell problems are avoided. The performance of smoothed SIBTEST is studied via simulation and real data analysis.

scholarly journals Effectiveness of Person Fit Indices in Item Response Models with Different Degrees of Item Local Dependence

2020 ◽  
Vol 14 (1) ◽  
pp. 41
Author(s):  
Yaqoub Z. Al Shaqsy ◽  
Yousef A. Abu Shindi ◽  
Rashid S. Almehrizi
Keyword(s):  
Item Response ◽  
Item Difficulty ◽  
Standard Normal Distribution ◽  
Local Dependence ◽  
Fit Indices ◽  
Person Fit ◽  
Response Models ◽  
Item Response Models ◽  
Weighted Index ◽  
Distributional Properties

This study aimed to examine the effectiveness of person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index) in item response models with different degrees of item local dependence (0.0, 0.3, 0.6, and 0.9) using simulated item parameters. Item responses for 40 samples each with 10000 subjects (a total of 400000 subjects) were simulated on a test of 60 items. Item discrimination parameters ranged between 0.19 and 1.79 and item difficulty parameters ranged between -2 and +2. 20% of test items were manipulated to show local dependence for each level of local dependence degrees. Student ability was generated to follow a standard normal distribution. Assumptions of item response theory were examined in all data sets using exploratory factor analysis and residual analysis using NOHARM platform for unidimensionality and Q3 index for local independence. Results showed that there was an increase in the percentages of non-conforming persons when increasing the degree of items local dependence for the three person fit indices (Wright’s weighted index, Drasgow index and Almehrizi’s weighted index). Results showed also that the percentages of non-conforming persons were larger with Wright’s weighted index than with Drasgow index and Almehrizi’s weighted index. The distributional properties of the three indices showed relatively consistent in distributional properties. Drasgow index and Almehrizi’s weighted index were very similar distributional properties. Also, there was a larger agreement index between Wright’s weighted index and Drasgow index.

Envelopes in multivariate regression models with nonlinearity and heteroscedasticity

Biometrika ◽  
2020 ◽  
Vol 107 (4) ◽  
pp. 965-981
Author(s):  
X Zhang ◽  
C E Lee ◽  
X Shao
Keyword(s):  
Dimension Reduction ◽  
Linear Models ◽  
Real Data ◽  
Estimation Procedure ◽  
Martingale Difference ◽  
Conditional Covariance ◽  
Conditional Mean ◽  
Model Free ◽  
Heteroscedastic Error ◽  
Multivariate Linear Models

Summary Envelopes have been proposed in recent years as a nascent methodology for sufficient dimension reduction and efficient parameter estimation in multivariate linear models. We extend the classical definition of envelopes in Cook et al. (2010) to incorporate a nonlinear conditional mean function and a heteroscedastic error. Given any two random vectors ${X}\in\mathbb{R}^{p}$ and ${Y}\in\mathbb{R}^{r}$, we propose two new model-free envelopes, called the martingale difference divergence envelope and the central mean envelope, and study their relationships to the standard envelope in the context of response reduction in multivariate linear models. The martingale difference divergence envelope effectively captures the nonlinearity in the conditional mean without imposing any parametric structure or requiring any tuning in estimation. Heteroscedasticity, or nonconstant conditional covariance of ${Y}\mid{X}$, is further detected by the central mean envelope based on a slicing scheme for the data. We reveal the nested structure of different envelopes: (i) the central mean envelope contains the martingale difference divergence envelope, with equality when ${Y}\mid{X}$ has a constant conditional covariance; and (ii) the martingale difference divergence envelope contains the standard envelope, with equality when ${Y}\mid{X}$ has a linear conditional mean. We develop an estimation procedure that first obtains the martingale difference divergence envelope and then estimates the additional envelope components in the central mean envelope. We establish consistency in envelope estimation of the martingale difference divergence envelope and central mean envelope without stringent model assumptions. Simulations and real-data analysis demonstrate the advantages of the martingale difference divergence envelope and the central mean envelope over the standard envelope in dimension reduction.

The Dark Tetrad

2015 ◽  
Vol 36 (4) ◽  
pp. 228-236 ◽  
Author(s):  
Janko Međedović ◽  
Boban Petrović
Keyword(s):  
Personality Traits ◽  
Antisocial Behavior ◽  
Second Order ◽  
The Other ◽  
Negative Pole ◽  
Latent Space ◽  
Order Factor

Abstract. Machiavellianism, narcissism, and psychopathy are personality traits understood to be dispositions toward amoral and antisocial behavior. Recent research has suggested that sadism should also be added to this set of traits. In the present study, we tested a hypothesis proposing that these four traits are expressions of one superordinate construct: The Dark Tetrad. Exploration of the latent space of four “dark” traits suggested that the singular second-order factor which represents the Dark Tetrad can be extracted. Analysis has shown that Dark Tetrad traits can be located in the space of basic personality traits, especially on the negative pole of the Honesty-Humility, Agreeableness, Conscientiousness, and Emotionality dimensions. We conclude that sadism behaves in a similar manner as the other dark traits, but it cannot be reduced to them. The results support the concept of “Dark Tetrad.”

Manipulate Me

2020 ◽  
Vol 36 (4) ◽  
pp. 554-562
Author(s):  
Alica Thissen ◽  
Frank M. Spinath ◽  
Nicolas Becker
Keyword(s):  
High School Students ◽  
Spatial Ability ◽  
Convergent Validity ◽  
Item Difficulty ◽  
Test Results ◽  
Response Elimination ◽  
School Students ◽  
Test Environment ◽  
Response Options ◽  
Construction Task

Abstract. The cube construction task represents a novel format in the assessment of spatial ability through mental cube rotation tasks. Instead of selecting the correct answer from several response options, respondents construct their own response in a computerized test environment, leading to a higher demand for spatial ability. In the present study with a sample of 146 German high-school students, we tested an approach to manipulate the item difficulties in order to create items with a greater difficulty range. Furthermore, we compared the cube task in a distractor-free and a distractor-based version while the item stems were held identical. The average item difficulty of the distractor-free format was significantly higher than in the distractor-based format ( M = 0.27 vs. M = 0.46) and the distractor-free format showed a broader range of item difficulties (.02 ≤  pi ≤ .95 vs. .37 ≤  pi ≤ .63). The analyses of the test results also showed that the distractor-free format had a significantly higher correlation with a broad intelligence test ( r = .57 vs. r = .17). Reasons for the higher convergent validity of the distractor-free format (prevention of response elimination strategies and the broader range of item difficulties) and further research possibilities are discussed.

Positional Estimation Within a Latent Space Model for Networks

Methodology ◽  
2006 ◽  
Vol 2 (1) ◽  
pp. 24-33 ◽  
Author(s):  
Susan Shortreed ◽  
Mark S. Handcock ◽  
Peter Hoff
Keyword(s):  
Random Effects ◽  
Network Data ◽  
Random Effects Models ◽  
Space Model ◽  
Network Analyses ◽  
Recent Advances ◽  
Latent Space ◽  
Latent Space Model ◽  
Modeling Data

Recent advances in latent space and related random effects models hold much promise for representing network data. The inherent dependency between ties in a network makes modeling data of this type difficult. In this article we consider a recently developed latent space model that is particularly appropriate for the visualization of networks. We suggest a new estimator of the latent positions and perform two network analyses, comparing four alternative estimators. We demonstrate a method of checking the validity of the positional estimates. These estimators are implemented via a package in the freeware statistical language R. The package allows researchers to efficiently fit the latent space model to data and to visualize the results.

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