How does Rasch modeling reveal difficulty and suitability level the fraction test question?

This article explains how to analyze test items in arithmetic operation with fractions to obtain the items' level of difficulty and fitness. Data were collected by using multiple-choice questions given to 50 fourth-grade students of an elementary school in Tasikmalaya city. The answers were then analyzed using the Rasch model and Winsteps 3.75 application, a combination of standard deviation (SD) and logit mean values (Mean). The score data of each person and question were used to estimate the pure score in the logit scale, indicating the level of difficulty of the test items. The categories were difficult (logit value +1 SD); very difficult (0.0 logit +1 SD); easy (0.0 logit -1 SD); very easy (logit value –SD). Three criteria were used to determine the level of difficulty and fitness of the questions: the Outfit Z-Standard/ZSTD value; Outfit Mean Square/MNSQ; and Point Measure Correlation. It resulted in a collection of test items suitable for use with several levels of difficulties, namely, difficult, very difficult, easy, and very easy, from the previous items, which had difficult, medium, and easy categories. Rasch model can help categorize questions and students' ability levels.

Validity and Reliability of Green Competencies Instrument for Automobile Technology Programme Using Rasch Model

This article aims to determine the validity of developed constructs and check the reliability of the newly developed instrument named as Questionnaire on Green Competencies for Automobile Engineering Technology (QGCAET) for the Automobile Technology Programme in Nigerian Universities. The instrument consists of 170 elements measuring four constructs namely Technical Green Competencies; Managerial Green Competencies; Personal Green Competencies and Social Green Competencies and was administered to 299 respondents made of Lecturers, Technologists and Final- Year Students of Automobile Engineering and Technology programme in Nigeria universities. The Rasch model was used to examine the validity and reliability of the items. From the analysis point of view, the polarity of the elements indicates that the correlation of the point measure (PTMEA CORR) of 170 elements of green competencies is between 0.00 and 0.55. The summary statistics show that the reliability of the items and the separation of the items of the green competencies instrument are 0.98 and 6.46, respectively. Similarly, the item reliability of each construct is between 0.96 and 0.99, and the reliability of the person is between 0.79 and 1.97, respectively. In terms of item fit statistics, a total of 157 items are found to be fit to achieve the objectives of the study. The result also indicates that the range of fit for the four (4) identified green competencies constructs is between 0.61 and 1.49 signifying that all the constructs are in harmony in measuring the items in the constructs, so suitable in achieving the objectives of the research.

The Factor Structure and Rasch Analysis of the Fear of COVID-19 Scale (FCV-19S) Among Chinese Students

The Fear of COVID-19 Scale (FCV-19S) is a new one-dimensional scale used to measure fear of an individual about the COVID-19. Given the seriousness of the COVID-19 situation in China when our study was taking place, our aim was to translate and examine the applicability of the FCV-19S in Chinese students. The sample used for validation comprised 2,445 Chinese students. The psychometrical characteristics of the Chinese FCV-19S (FCV-19S-C) were tested using Rasch analysis. Principal component analysis (PCA) proved the unidimensional structure of the model. Both infit and outfit mean square (MNSQ) values (0.69–1.31) and point-measure correlations (0.82–0.86) indicated a good model fit. Person-item separation and reliability values indicated good reliability of the scale. The person-item map revealed an acceptable level of match between the persons and the items. Differential item functioning of the FCV-19S-C showed no differences with respect to age or gender. FCV-19S-C scores were significantly associated with anxiety, stress, depression, ego-resilience, and general health. The FCV-19S-C was proven to be effective in measuring fear of Chinese students about the COVID-19.

What Is a Flare? The Manitoba Living With IBD Study

Background Flare is a poorly defined term used by patients and clinicians to indicate inflammatory bowel disease (IBD) status. This study aimed to evaluate the validity of a single-item 7-point flare indicator relative to other measures of disease flare. Methods The longitudinal Manitoba Living with IBD Study followed persons with IBD for 1 year; they completed biweekly online surveys and provided 3 stool samples. Disease flare on a single-item flare indicator with 7 possible responses developed for the study was defined by report of symptoms as “moderately” or “much” worse. The flare indicator was evaluated against 5 measures of disease activity: fecal calprotectin score (FCAL), a 2-point disease status indicator, a 4-point flare certainty indicator, the IBD Symptom Index short form (SIBDSI), and the short form IBD Questionnaire (SIBDQ). Participants in a flare, based on the 7-point measure, were matched to a nonflaring participant, and a stool sample was collected. Results Of the 155 IBD participants, almost half (n = 74) experienced a flare. Of those who flared, 97.0% endorsed active IBD on the 2-point indicator (controls 42.5%; P < .001); 91.9% endorsed active IBD on the 4-point certainty indicator (controls 32.9%; P < .001); 90.5% endorsed active disease on the SIBDSI (controls 34.2%; P < .001); and 48.5% had an elevated FCAL (controls 34.3%; P < .05). The mean SIBDQ was lower for the flare group compared with controls (43.9 [SD 11.1] vs 58.3 [SD 8.5]; P < .001), indicating worse disease. Conclusions The 7-point flare indicator robustly identified symptomatic flares. This patient self-report indicator reflected meaningful changes in more complex clinical indices and had only weak concordance with the presence of inflammation.

Evaluating Construct Validity and Reliability of Intention to Transfer Training Conduct Instrument Using Rasch Model Analysis

The impact of the Industry Revolution 4.0 (IR4.0) in the workplace requires organisations to ensure clerical employees can effectively transfer their newly acquired knowledge and skills learned in training back into the workplace. Hence, an instrument is required to identify factors influencing the intention to transfer training conduct amongst clerical employees. Thus, this paper presents the evaluation of construct validity and reliability of the new instrument to confirm its objectivity and clarity in measuring the constructs under study as intended. This four-point Likert-type scale instrument consists of 72 self-assessment items that represent 12 constructs. The Rasch Model was then employed to analyse the construct validity and reliability by evaluating the suitability of items in the respective constructs on the instrument. The item and person reliability and strata indices, point-measure correlation, and outfit mean square values were examined. The analysis found that three constructs in the item and person reliability index and eight constructs in the item and person reliability strata index were low but adequate and met the Rasch Model measurement acceptable level. Meanwhile, point-measure correlation values for all constructs fulfilled the criteria. Finally, the outfit mean square values established that 65 items in the constructs were found to be fit, whereas seven items were misfits which require improvement. Subsequently, the seven misfit items were improved as the item and person reliability values could be increased, thus the items were retained. Thereafter, the instrument was ready to be used for data collection in the actual study.

On approximations of the point measures associated with the Brownian web by means of the fractional step method and the discretization of the initial interval

UDC 519.21 We establish the rate of weak convergence in the fractional step method for the Arratia flow in terms of the Wasserstein distance between the images of the Lebesque measure under the action of the flow. We introduce finite-dimensional densities that describe sequences of collisions in the Arratia flow and derive an explicit expression for them. With the initial interval discretized, we also discuss the convergence of the corresponding approximations of the point measure associated with the Arratia flow in terms of such densities.

On the Zeros of Non-Analytic Random Periodic Signals

In this paper, we investigate the local universality of the number of zeros of a random periodic signal of the form $S_n(t)=\sum _{k=1}^n a_k f(k t)$, where $f$ is a $2\pi -$periodic function satisfying weak regularity conditions and where the coefficients $a_k$ are i.i.d. random variables, which are centered with unit variance. In particular, our results hold for continuous piecewise linear functions. We prove that the number of zeros of $S_n(t)$ in a shrinking interval of size $1/n$ converges in law as $n$ goes to infinity to the number of zeros of a Gaussian process whose explicit covariance only depends on the function $f$ and not on the common law of the random coefficients $(a_k)$. As a byproduct, this entails that the point measure of the zeros of $S_n(t)$ converges in law to an explicit limit on the space of locally finite point measures on $\mathbb R$ endowed with the vague topology. The standard tools involving the regularity or even the analyticity of $f$ to establish such kind of universality results are here replaced by some high-dimensional Berry–Esseen bounds recently obtained in [ 7]. The latter allow us to prove functional Central Limit Theorems in $C^1$ or Lipschitz topology in situations where usual criteria cannot be applied due to the lack of regularity.

Epiphytic bryophyte biomass estimation on tree trunks and upscaling in tropical montane cloud forests

Epiphytic bryophytes (EB) are some of the most commonly found plant species in tropical montane cloud forests, and they play a disproportionate role in influencing the terrestrial hydrological and nutrient cycles. However, it is difficult to estimate the abundance of EB due to the nature of their “epiphytic” habitat. This study proposes an allometric scaling approach implemented in twenty-one 30 × 30 m plots across an elevation range in 16,773 ha tropical montane cloud forests of northeastern Taiwan to measure EB biomass, a primary metric for indicating plant abundance and productivity. A general allometry was developed to estimate EB biomass of 100 cm2 circular-shaped mats (n = 131) with their central depths. We developed a new point-intercept instrument to rapidly measure the depths of EB along tree trunks below 300 cm from the ground level (sampled stem surface area (SSA)) (n = 210). Biomass of EB of each point measure was derived using the general allometry and was aggregated across each SSA, and its performance was evaluated. Total EB biomass of a tree was estimated by referring to an in-situ conversion model and was interpolated for all trees in the plots (n = 1451). Finally, we assessed EB biomass density at the plot scale of the study region. The general EB biomass-depth allometry showed that the depth of an EB mat was a salient variable for biomass estimation (R2 = 0.72, p < 0.001). The performance of upscaling from mats to SSA was satisfactory, which allowed us to further estimate mean (±standard deviation) EB biomass of the 21 plots (272 ± 104 kg ha−1). Since a significant relationship between tree size and EB abundance is commonly found, regional EB biomass may be mapped by integrating our method and three-dimensional remotely sensed airborne data.

Optimal stopping for measure-valued piecewise deterministic Markov processes

This paper investigates the random horizon optimal stopping problem for measure-valued piecewise deterministic Markov processes (PDMPs). This is motivated by population dynamics applications, when one wants to monitor some characteristics of the individuals in a small population. The population and its individual characteristics can be represented by a point measure. We first define a PDMP on a space of locally finite measures. Then we define a sequence of random horizon optimal stopping problems for such processes. We prove that the value function of the problems can be obtained by iterating some dynamic programming operator. Finally we prove via a simple counter-example that controlling the whole population is not equivalent to controlling a random lineage.

Quantification of the pace of biological aging in humans through a blood test, the DunedinPoAm DNA methylation algorithm

Biological aging is the gradual, progressive decline in system integrity that occurs with advancing chronological age, causing morbidity and disability. Measurements of the pace of aging are needed as surrogate endpoints in trials of therapies designed to prevent disease by slowing biological aging. We report a blood-DNA-methylation measure that is sensitive to variation in pace of biological aging among individuals born the same year. We first modeled change-over-time in 18 biomarkers tracking organ-system integrity across 12 years of follow-up in n = 954 members of the Dunedin Study born in 1972–1973. Rates of change in each biomarker over ages 26–38 years were composited to form a measure of aging-related decline, termed Pace-of-Aging. Elastic-net regression was used to develop a DNA-methylation predictor of Pace-of-Aging, called DunedinPoAm for Dunedin(P)ace(o)f(A)ging(m)ethylation. Validation analysis in cohort studies and the CALERIE trial provide proof-of-principle for DunedinPoAm as a single-time-point measure of a person’s pace of biological aging.