Modeling local item dependence with the hierarchical generalized linear model

Local item dependence (LID) can emerge when the test items are nested within common stimuli or item groups. This study proposes a three-level hierarchical generalized linear model (HGLM) to model LID when LID is due to such contextual effects. The proposed three-level HGLM was examined by analyzing simulated data sets and was compared with the Rasch-equivalent two-level HGLM that ignores such a nested structure of test items. The results demonstrated that the proposed model could capture LID and estimate its magnitude. Also, the two-level HGLM resulted in larger mean absolute differences between the true and the estimated item difficulties than those from the proposed three-level HGLM. Furthermore, it was demonstrated that the proposed three-level HGLM estimated the ability distribution variance unaffected by the LID magnitude, while the two-level HGLM with no LID consideration increasingly underestimated the ability variance as the LID magnitude increased.     

Formulating latent growth using an explanatory item response model approach

In this paper, we present a way to extend the Hierarchical Generalized Linear Model (HGLM; Kamata (2001), Raudenbush (1995)) to include the many forms of measurement models available under the formulation known as the Random Coefficients Multinomial Logit (MRCML) Model (Adams, Wilson and Wang, 1997), and apply that to growth modeling. First, we review two different traditions in modeling growth studies: the first is based in the hierarchical linear modeling (HLM) tradition, and the second, which is the topic of this paper, is rooted in the Rasch measurement tradition - this is the linear Latent Growth Item Response Model (LG-IRM). Going beyond the linear case, the LG-IRM approach allows us to considerably extend the range of models available in the HLM tradition to incorporate several of the extensions of IRT models that are used in creating explanatory item response models (EIRM; De Boeck and Wilson, 2004). We next present a number of extensions - including polynomial growth modeling, differential item functioning (DIF) effects, growth functions that can be approximated by polynomial expressions, provision for polytomous responses, person and item covariates (and time varying covariates), and multiple dimensions of growth. We provide two empirical examples to illustrate several of the models, using the ConQuest software (Wu, Adams, Wilson and Haldane, 2008) to carry out the analyses. We also provide several simulations to investigate the success of the estimation procedures.     

An examination of exposure control and content balancing restrictions on item selection in CATs using the partial credit model

The purpose of the present investigation was to systematically examine the effectiveness of the Sympson-Hetter technique and rotated content balancing relative to no exposure control and no content rotation conditions in a computerized adaptive testing system (CAT) based on the partial credit model. A series of simulated fixed and variable length CATs were run using two data sets generated to multiple content areas for three sizes of item pools. The 2 (exposure control) X 2 (content rotation) X 2 (test length) X 3 (item pool size) X 2 (data sets) yielded a total of 48 conditions. Results show that while both procedures can be used with no deleterious effect on measurement precision, the gains in exposure control, pool utilization, and item overlap appear quite modest. Difficulties involved with setting the exposure control parameters in small item pools make questionable the utility of the Sympson-Hetter technique with similar item pools.     

Effects of varying magnitude and patterns of response dependence in the unidimensional Rasch model

By adding items with responses identical to a selected item, Smith (2005) investigated the effect of the response dependence on person and item parameter estimates in the dichotomous Rasch model. By varying the magnitude of response dependence among selected items, rather than their having perfect dependence, this paper provides additional insights into the effects of response dependence on the same estimates in the same model. Two sets of simulations are reported. In the first set, responses to all items except the first were dependent on either the first item or on the immediately preceding item; in the second set, subsets of items were formed first, and then within each of these subsets, responses to all items in a subset except the first were dependent on either the first item or on the immediately preceding item. The effects of dependence were noticeable in all of the statistics reported. In particular, the fit statistics and the parameter estimates showed increasing discrepancies from their theoretical values as a function of the magnitude of the dependence. In some cases, however, two related statistics gave the impression of improvement as a function of increased dependency; first the standard deviation of person estimates showed an increase, and second the index analogous to traditional reliability showed relative increase. In addition to the estimates and depending on the structure and magnitude of the dependence, the person distribution was affected systematically, ranging from becoming skewed to becoming bimodal. The effects on the distribution help explain some of the effects on the statistics reported. In the case of the second set of simulations in which the dependence is within subsets of items, it is possible to take account of the response dependence. This is done by summing the responses of the items within each subset to form a polytomous item and then analyzing the data in terms of a smaller number of polytomous items. This way of accounting for dependence, in which the maximum score for the test as a whole remains the same, gives a more accurate value of the reliability and a more realistic distribution of the person estimates than when the dependence within subsets of items is not taken into account.     

Formalizing dimension and response violations of local independence in the unidimensional Rasch model

Local independence in the Rasch model can be violated in two generic ways that are generally not distinguished clearly in the literature. In this paper we distinguish between a violation of unidimensionality, which we call trait dependence, and a specific violation of statistical independence, which we call response dependence, both of which violate local independence. Distinct algebraic formulations for trait and response dependence are developed as violations of the dichotomous Rasch model, data are simulated with varying degrees of dependence according to these formulations, and then analysed according to the Rasch model assuming no violations. Relative to the case of no violation it is shown that trait and response dependence result in opposite effects on the unit of scale as manifested in the range and standard deviation of the scale and the standard deviation of person locations. In the case of trait dependence the scale is reduced; in the case of response dependence it is increased. Again, relative to the case of no violation, the two violations also have opposite effects on the person separation index (analogous to Cronbach's alpha reliability index of traditional test theory in value and construction): it decreases for data with trait dependence; it increases for data with response dependence. A standard way of accounting for dependence is to combine the dependent items into a higher-order polytomous item. This typically results in a decreased person separation index index and Cronbach's alpha, compared with analysing items as discrete, independent items. This occurs irrespective of the kind of dependence in the data, and so further contributes to the two violations not being distinguished clearly. In an attempt to begin to distinguish between them statistically this paper articulates the opposite effects of these two violations in the dichotomous Rasch model.     

Equating and item banking with the Rasch model

This article describes Rasch measurement procedures for equating multiple test forms or calibrating an item bank. The procedures entail (a) selecting an appropriate data collection design, (b) estimating parameters, (c) transforming the parameters from multiple forms to a common scale, and (d) evaluating the quality of the linkage between these forms. Data collection designs include (a) anchor tests, (b) single group, (c) single data set, and (d) equivalent groups. Estimation procedures may involve (a) separate or (b) simultaneous calibration of data from multiple forms. Transformation is typically accomplished using (a) estimation scaling, but may involve (b) parameter anchoring or (c) computing equating constants. Link quality is evaluated using four fit indices: (a) item-within-link, (b) item-between-link, (c) link-within-bank, and (d) form-within-bank. These procedures are illustrated using an anchor test design.     

Design parameter selection in the presence of noise

Themethod of imprecision is a design method whereby a multi-objective design problem is resolved by maximizing the overall degree ofdesigner preference: values are iteratively selected based on combining the degree of preference placed on them. Consider, however, design problems that exhibit multiple uncertainty forms (noise). In addition to degrees of preference(imprecision) there areprobabilistic uncertainties caused by, for example, measuring and fabrication limitations. There are also parameters that can take on any valuepossible within a specified range, such as a manufacturing or tuning adjustment. Finally, there may be parameters which mustnecessarily satisfly all values within the range over which they vary, such as a horsepower requirement over a motor's different speeds. This paper defines a best set of design parameters for design problems with such multiple uncertainty forms and requirements.     

Using LinLog and FACETS to model item components in the LLTM

The current study investigates the performance of two Rasch measurement programs and their parameter estimations on the linear logistic test model (LLTM; Fischer, 1973). These two programs, LinLog (Whitely & Nieh, 1981) and FACETS (Linacre, 2002), are used to investigate within-item complexity factors in a spatial memory measure tool. LinLog uses conditional maximum likelihood to estimate person and item parameters and is an LLTM specific program. FACETS is usually reserved for the many-facet Rasch model (MFRM; Linacre, 1989), however in the case of specifically designed within-item solution processes, a multifaceted approach makes good sense. It is possible to consider each dimension within the item as a separate facet, just as if there were multiple raters for each item. Simulations of 500 and 1000 persons expand the original data set (114 persons) to better examine each estimation technique. LinLog and FACETS analyses show strikingly similar results in both the simulation and original data conditions, indicating that the FACETS program produces accurate LLTM parameter estimates.     

Dynamic accommodation response in the presence of astigmatism

It has been suggested that in the presence of astigmatism some individuals make cyclic changes in focus over the astigmatic interval to obtain better visual performance. The aim in the present study was to identify such cyclic accommodative behavior and to characterize the variability of the response in the presence of astigmatism. The dynamic accommodation response in the presence of induced astigmatism was recorded objectively with an infrared optometer in seven young adults. Astigmatism led directly to increased accommodative variability in certain individuals. In two of seven participants there was evidence for aperiodic cyclic accommodative responses between different portions of the astigmatic interval. However, the amplitude of these tracking responses was much smaller than the astigmatic interval.     

Unique properties of Rasch model item information functions

The Rasch family of models displays several well-documented properties that distinguish them from the general item response theory (IRT) family of measurement models. This paper describes an additional unique property of Rasch models, referred to as the property of item information constancy. This property asserts that the area under the information function for Rasch models is always equal to the number of response categories minus one, regardless of the values of the item location parameters. The implication of the property of item information constancy is that, for a given number of response categories, all items following a Rasch model contribute equally to the height of the test information function across the entire latent continuum.     

A framework for the selection of idle vehicle home locations in an automated guided vehicle system

In the study of automated guided vehicles systems (AGVS), one assumption often made in the management of vehicles is the existence of either home locations or a circulatory loop to buffer or hold idle vehicles. A review of AGVS literature reveals that different researchers pursue one idle vehicle management policy or the other. In some studies, idle vehicles are assumed to circulate in some loops in the system while others assume they are routed to some dwell point locations where they are held until they are reassigned. When the dwell point option is implemented, different strategies for implementation are also available. However, what is generally lacking in references to dwell point strategies are the techniques for selecting the optimal or best dwell points for a given facility. In this study, the problem of dwell point or home location specification is addressed. The problem was modelled mathematically to determine the optimal home locations. The emphasis in the paper is on a unidirectional AGVS guide path. The criterion of optimization employed is the minimization of the system response time to vehicle demand points when dispatched from home locations. Solution methodologies are presented and example problems solved to illustrate the applications of the models presented.     

Examining item difficulty and response time on perceptual ability test items

This study examined item calibration stability in relation to response time and the levels of item difficulty between different response time groups on a sample of 389 examinees responding to six different subtest items of the Perceptual Ability Test (PAT). The results indicated that no Differential Item Functioning (DIF) was found and a significant correlation coefficient of item difficulty was formed between slow and fast responders. Three distinct levels of difficulty emerged among the six subtests across groups. Slow responders spent significantly more time than fast responders on the four most difficult subtests. A positive significant relationship was found between item difficulty and response time across groups on the overall perceptual ability test items. Overall, this study found that: 1) the same underlying construct is being measured across groups, 2) the PAT scores were equally useful across groups, 3) different sources of item difficulty may exist among the six subtests, and 4) more difficult test items may require more time to answer.     

Coupling of cell fate selection model enhances DNA damage response and may underlie BE phenomenon

Double‐strand break‐induced (DSB) cells send signal that induces DSBs in neighbour cells, resulting in the interaction among cells sharing the same medium. Since p53 network gives oscillatory response to DSBs, such interaction among cells could be modelled as an excitatory coupling of p53 network oscillators. This study proposes a plausible coupling model of three‐mode two‐dimensional oscillators, which models the p53‐mediated cell fate selection in globally coupled DSB‐induced cells. The coupled model consists of ATM and Wip1 proteins as variables. The coupling mechanism is realised through ATM variable via a mean‐field modelling the bystander signal in the intercellular medium. Investigation of the model reveals that the coupling generates more sensitive DNA damage response by affecting cell fate selection. Additionally, the authors search for the cause‐effect relationship between coupled p53 network oscillators and bystander effect (BE) endpoints. For this, they search for the possible values of uncertain parameters that may replicate BE experiments’ results. At certain parametric regions, there is a correlation between the outcomes of cell fate and endpoints of BE, suggesting that the intercellular coupling of p53 network may manifest itself as the form of observed BEs.Inspec keywords: biological effects of ionising particles, molecular biophysics, biochemistry, DNA, cellular biophysics, physiological models, biomolecular effects of radiation, cellular effects of radiation, biological effects of X‐rays, oscillations, proteinsOther keywords: three‐mode two‐dimensional oscillators, p53‐mediated cell fate selection, globally coupled DSB‐induced cells, coupled model consists, coupling mechanism, ATM variable, bystander signal, intercellular medium, sensitive DNA damage response, coupled p53 network oscillators, intercellular coupling, cell fate selection model, double‐strand break‐induced cells, DSBs, neighbour cells, oscillatory response, excitatory coupling, plausible coupling model     

Identified and unidentified cases of the fixed-effects 3- and 4-parameter models in item response theory

The 3-parameter logistic (3PL) model including guessing parameters is one of the popular models in item response theory. While the guessing parameters in the fixed-effects 3PL model with non-stochastic abilities have been believed to have identification, some counter examples with new ones given in this paper are currently available. In this paper, the concept of degeneracy for nested models is introduced. Some degenerate cases in the counter examples are shown to have model identification for guessing parameters, which are further shown to have model unidentification in a more degenerate model. Similar results in the fixed-effects 4-parameter logistic model are also derived.

     

SNR and SINR-based selection combining algorithms in the presence of arbitrarily distributed co-channel interferers

The performance of selection combining (SC) diversity in the presence of additive white Gaussian noise as well as multiple co-channel interfering signals over fading channels is analysed. The analysis considers two SC algorithms, namely, the signal-to-noise ratio-(SNR) based SC algorithm and the signal-to-interference-plus-noise ratio (SINR)-based SC algorithm. Closed-form expressions for the distribution of the resulting SINR and the outage probability performance are derived for both SC algorithms. The derived expressions are valid for arbitrary number of interfering signals, and when the desired signal replicas experience independent Rayleigh fading with generalised statistics. In addition, they are applicable for the general case when the interfering signals are subject to arbitrary fading models, which include the cases of identical, non-identical, correlated and mixed-mode fading scenarios. Numerical results are presented to examine the impact of different fading conditions and system parameters on the outage performance for both SC algorithms under consideration.     

Flux flow noise power spectra in the presence of local pinning interactions

We derive expressions for the dc flux flow voltage and for the flux flow noise power spectrum in type II superconductors using a model in which flux bundles travel a distance1 less than the sample widthL before being stopped for finite times by local pinning interactions. The frequency dependence of the power spectrum is shown to be identical to our earlier derivation, where we assumed that pinning and release of flux bundles occurred in zero times, an assumption we now show to be incorrect. This frequency dependence has been shown to lead to good agreement for experimentally measured transit times, which have repeatedly been shown to be too short when obtained from models of uninter-rupted flux transit across the sample width. The concept of a pinned fraction arises naturally in our model, and occurs because of two factors; first, in certain regions the Lorentz force is not sufficient to overcome pinning, and second, in regions where flux flow occurs, fluxoids will be held up for brief periods because of interaction with local pinning centers. The expressions for the noise power at zero frequency and the dc voltage are modified by factors that depend on averages of1.Research supported by U.S. ERDA Grant No. E(11–1) 2890.     

Numerical modeling of precessing vortex core in the presence of local heat sources

Based on the results of numerical simulation of a nonstationary, nonaxisymmetric turbulent swirling gas flow in a tube with local sources of heat release, it is shown that a precessing vortex core (PVC) appears at supercritical values of the swirl parameter as a result of the development of instability of a left-handed bending mode. The dependence of the PVC frequency on the mass flow rate of the gas and the heat-source power has been studied. As the heat-source power increases, the frequency of precession grows while the amplitude of vortex core oscillations drops.     

Continuum topology optimization considering uncertainties in load locations based on the cloud model

Few researchers have paid attention to designing structures in consideration of uncertainties in the loading locations, which may significantly influence the structural performance. In this work, cloud models are employed to depict the uncertainties in the loading locations. A robust algorithm is developed in the context of minimizing the expectation of the structural compliance, while conforming to a material volume constraint. To guarantee optimal solutions, sufficient cloud drops are used, which in turn leads to low efficiency. An innovative strategy is then implemented to enormously improve the computational efficiency. A modified soft-kill bi-directional evolutionary structural optimization method using derived sensitivity numbers is used to output the robust novel configurations. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed algorithm.     

Blood response to plasticized poly(vinyl chloride): dependence of fibrinogen adsorption on plasticizer selection and surface plasticizer level

The high level of plasticizer in plasticized poly(vinyl chloride) (PVC) ensures that plasticizer selection has an important influence on the suitability of PVC to function in blood-contacting applications. In this study, three types of plasticized PVC in sheet form, with di-(2-ethylhexyl)phthalate (DEHP), tri-(2-ethylhexyl)trimellitate (TEHTM) and n-butyryltri-n-hexyl citrate (BTHC) as plasticizer, were selected for assessment and single solute fibrinogen adsorption was utilized as an initial index of interactions with blood components. Fibrinogen adsorption behavior shows a strong dependence on the plasticizer selection, plasticizer level at the surface and the adsorption conditions, such as adsorption time and fibrinogen solution concentration. Results indicate that BTHC plasticized PVC possesses the lowest adsorption capacity in the three types of plasticized PVC, while TEHTM plasticized PVC seems to have the strongest reactivity in certain fibrinogen solution concentrations. The alteration of surface plasticizer level was achieved by a methanol-cleaning treatment with a variety of cleaning times and the fibrinogen adsorption on plasticized PVC decreases with the reduction of surface plasticizer level. The migration behavior of two phthalate esters (DEHP and TEHTM) was evaluated using UV-Spectrophotometer to determine the plasticizer level at the surfaces. In addition, the fibrinogen adsorption mechanism was examined with Freundlich adsorption modeling.