Three-parameter Logistic Model Research Articles

Analysis of Quality of Critical Thinking Skills Test Based on Item Response Theory Using R-Program

This research aims to describe the quality of critical thinking skill test of fluid mechanics material in senior high schools in Makassar City. The emphasis is the content validity aspect, the characteristics of each item for the One-Parameter Logistic (1PL) model, the Two-Parameter Logistic (2PL) model, dan the Three-Parameter Logistic (3PL) model. It is a descriptive quantitative research with the subject of all student responses to the critical thinking skills test of fluid mechanics material at senior high schools in Makassar City. There were 726 student responses. The data were collected online by google form and analyzed by using descriptive quantitative technique. The results showed that the critical thinking skill test of fluid mechanics material had fulfilled the content validity. Analysis of the quality of CTS test items showed that the models of 1PL, 2PL, and 3PL were all consistent, showing that the test items were mostly able to discriminate the high abilitytestees from the low abilitytestees. Of the three logistic model approaches used to estimate the parameters of item difficulty level, item discrimination, and guess factor, the 3PL model is better than the other twomodels.

The Effect of the Percentage of Missing Data on Estimating the Standard Error of the Items' Parameters and the Test Information Function According to the Three-Parameter Logistic Model in the Item Response Theory

This study aimed to investigate the effect of the percentage of missing data on estimating the standard error of the items' parameters and the test information function based on the three-parameter model using generated data. To achieve the objectives of the study, (1000) examinees' responses were generated on a test consisting of (50) dichotomous items according to the three-parameter logistic model( 3PL) using (WINGEN3) software. By using (SPSS) and (EXCEL), data containing missing responses were obtained at the percentages of (0%, 5%, 10%, 15%). Four files were prepared that include the missing four percentages. The items' parameters for these files were identified, , the items and individuals were fitted for ( 3PL-IRT), number of persons were removed. The results of the study showed that there are statistically significant differences between the means of the standard errors for estimating the difficulty and the discrimination parameter of the test based on the three-parameter model according to the difference in the missing data percentages of (0%, 5%, 10%, 15%) and in favor of the lesser missing percentages, which means that the fewer missing percentages are, it is expected that the standard error value will decrease in estimating the difficulty and the discrimination parameter of the item, and that the best missing data percentage was (5%). The results also indicated that the information function increases as the missing data percentage decreases.

A General Three-Parameter Logistic Model With Time Effect.

Within the framework of item response theory, a new and flexible general three-parameter logistic model with response time (G3PLT) is proposed. The advantage of this model is that it can combine time effect, ability, and item difficulty to influence the correct-response probability. In contrast to the traditional response time models used in educational psychology, the new model incorporates the influence of the time effect on the correct-response probability directly, rather than linking them through a hierarchical method via latent and speed parameters as in van der Linden's model. In addition, the Metropolis–Hastings within Gibbs sampling algorithm is employed to estimate the model parameters. Based on Markov chain Monte Carlo output, two Bayesian model assessment methods are used to assess the goodness of fit between models. Finally, two simulation studies and a real data analysis are performed to further illustrate the advantages of the new model over the traditional three-parameter logistic model.

QUALITY AND FEATURE OF MULTIPLE-CHOICE QUESTIONS IN EDUCATION

The quality of multiple-choice questions (MCQs) as well as the student's solve behavior in MCQs are educational concerns. MCQs cover wide educational content and can be immediately and accurately scored. However, many studies have found some flawed items in this exam type, thereby possibly resulting in misleading insights into students’ performance and affecting important decisions. This research sought to determine the characteristics of MCQs and factors that may affect the quality of MCQs by using item response theory (IRT) to evaluate data. For this, four samples of different sizes from US and China in secondary and higher education were chosen. Item difficulty and discrimination were determined using item response theory statistical item analysis models. Results were as follows. First, only a few guessing behaviors are included in MCQ exams because all data fit the two-parameter logistic model better than the three-parameter logistic model. Second, the quality of MCQs depended more on the degree of training of examiners and less on middle or higher education levels. Lastly, MCQs must be evaluated to ensure that high-quality items can be used as bases of inference in middle and higher education. Keywords: higher education, item evaluation, item response theory, multiple-choice test, secondary education

A three-parameter logistic regression model

Dose–response experiments and data analyses are often carried out according to an optimal design under a model assumption. A two-parameter logistic model is often used because of its nice mathematical properties and plausible stochastic response mechanisms. There is an extensive literature on its optimal designs and data analysis strategies. However, a model is at best a good approximation in a real-world application, and researchers must be aware of the risk of model mis-specification. In this paper, we investigate the effectiveness of the sequential ED-design, the D-optimal design, and the up-and-down design under the three-parameter logistic regression model, and we develop a numerical method for the parameter estimation. Simulations show that the combination of the proposed model and the data analysis strategy performs well. When the logistic model is correct, this more complex model has hardly any efficiency loss. The three-parameter logistic model works better than the two-parameter logistic model in the presence of model mis-specification.

Is It Worthy to Take Account of the “Guessing” in the Performance of the Raven Test? Calling for the Principle of Parsimony for Test Validation

The present study compares the fit of two- and three-parameter logistic (2PL and 3PL) models of item response theory in the performance of preschool children on the Raven’s Colored Progressive Matrices. The test of Raven is widely used for evaluating nonverbal intelligence of factor g. Studies comparing models with real data are scarce on the literature and this is the first to compare models of two and three parameters for the test of Raven, evaluating the informational gain of considering guessing probability. Participants were 582 Brazilian’s preschool children ( Mage = 57 months; SD = 7 months; 46% female) who responded individually to the instrument. The model fit indices suggested that the 2PL fit better to the data. The difficulty and ability parameters were similar between the models, with almost perfect correlations. Differences were observed in terms of discrimination and test information. The principle of parsimony must be called for comparing models.

Comparison of the Accuracy of Item Response Theory Models in Estimating Student’s Ability

This study aims to determine the item response theory model which is more accurate in estimating students' mathematical abilities. The models compared in this study are Multiple Choice Model and Three-Parameter Logistic Model. Data used in this study are the responses of a mathematical test of 1704 eighth-grade junior high school students from six schools in the Depok City, West Java. The Sampling is done by using a purposive random sampling technique. The mathematics test used for research data collection consisted of 30 multiple choice format items. After the data is obtained, Research hypotheses were tested using the variance test method (F-test) to find out which model is more accurate in estimating ability parameters. The results showed that Fvalue is obtained 1.089, and Ftable is 1.087, the value of Fvalue > Ftable, so it concluded that Ho rejected. That means Multiple Choice Model is more accurate than Three-Parameter Logistic Model in estimating the parameters of students' mathematical abilities. This makes the Multiple-Choice Model a recommended model for estimating mathematical ability in MC item format tests, especially in the field of mathematics and other fields that have similar characteristics.

A methodological approach to assess canopy NDVI–based tomato dynamics under irrigation treatments

A tomato field experiment under deficit irrigation treatments was established to assess the feasibility of nonlinear mixed models to predict the change in the canopy Normalized Difference Vegetation Index (NDVI) along the growing season. The irrigation doses were 50, 70, 85, and 100 % of the actual evapotranspiration (ETc). The experiment was performed in the Peruvian Arid Coastal Region (13.10 S, 76.37 W). On-ground destructive plant measurements (7 times) allowed to obtain the leaf area index (LAI) and the canopy equivalent water thickness (EWTcanopy) to validate the experiment. Similarly, volumetric soil moisture was monitored at three hours interval using time-domain reflectometry. High-resolution multispectral imagery was acquired along the growing season (10 times) using an unmanned aerial vehicle. NDVI at plant level was obtained based on oversegmented imagery. The canopy NDVI growth curves were obtained in relation to the irrigation treatments and growing degree days (GDD) using a nonlinear mixed model.Deficit irrigation doses (50, 70 and 85 % ETc) induced lower biomass accumulation and greatly affected LAI and EWTcanopy, attaining lower values (p < 0.05) than the control (100 % ETc). In spite of reaching higher LAI and EWTcanopy values, 70 % ETc was not significantly different from 50 % ETc (p < 0.05) showing the difficulty to accurately discriminate treatments with high deficit irrigation; 85 % ETc produced important differences on EWTcanopy and LAI compared to the other deficit irrigation treatments (p < 0.05) due to a higher leaf area expansion. Deficit irrigation doses led to less vigorous plants resulting in lower NDVI compared to the control. Notwithstanding 50 % ETc obtained lower NDVI values than 70 % ETc, differences were not significant. Volumetric soil moisture was consistent with the irrigation treatments, resulting in a decreased trend with decreasing water application along the growing season. A three-parameter logistic mixed model was found to be well-suited to fit the tomato canopy NDVI growth curves in function of the irrigation treatments (i.e. fixed effects) considering the plant-specific variability (i.e. random effects). At maturity stage, significant differences of the deficit irrigation treatments from the control were obtained (p < 0.05) when cumulative effect of the treatments was well-defined and NDVI reached asymptotic behavior. During the vegetative stage, the inflection point marked the fastest NDVI growth rate for the 100 % ETc treatment whereas the lowest for the 50 % ETc (p < 0.05). The diagnosis plots and the low root mean squared error of the residuals indicated the suitability of using the three-parameter logistic growth curve estimated as a nonlinear mixed model to predict NDVI.

Estimating standard errors of IRT true score equating coefficients using imputed item parameters

Reporting standard errors of equating has been advocated as a standard practice when conducting test equating. The two most widely applied procedures for standard errors of equating including the bootstrap method and the delta method are either computationally intensive or confined to the derivations of complicated formulas. In the current study, a hypothetical example was used to illustrate how the multiple imputation method could be taken as an alternative procedure for obtaining the standard errors for the item response theory (IRT) true score equating coefficients in the context of the common-item nonequivalent groups equating design under the three-parameter logistic IRT model. This method makes use of multiple sets of imputed item parameter values. By using the simulated and real data, the performance of the multiple imputation method was examined and compared with that of the bootstrap and delta methods. The results indicated that the multiple imputation method performed as effectively as the bootstrap method and the delta method when using the characteristic curve methods. The multiple imputation method produced very similar results to the delta method when the moment methods were used.

Choosing between CDM and Unidimensional IRT: The Proportional Reasoning Test Case

ABSTRACT Cognitive diagnosis models (CDMs) have gained increasing popularity recently because of their potential to provide diagnostic inferences that can inform learning and teaching. However, the development of cognitive diagnostic assessments (CDAs) is lagging behind the development of the associated psychometric models. At present, it is not clear whether and how much extra information can be obtained by analyzing CDA data with a CDM rather than simply using unidimensional item response theory models. This study fits CDMs and three-parameter logistic (3PL) model to the data from a CDA. Results showed that the CDMs fitted the data well, but the 3PL model did not. Compared with the 3PL model, the CDMs can highlight student differences from a multidimensional perspective, thus offering finer-grained information that unidimensional IRT models are not capable of providing.

Analysing Standard Progressive Matrices (SPM-LS) with Bayesian Item Response Models.

Raven’s Standard Progressive Matrices (SPM) test and related matrix-based tests are widely applied measures of cognitive ability. Using Bayesian Item Response Theory (IRT) models, I reanalyzed data of an SPM short form proposed by Myszkowski and Storme (2018) and, at the same time, illustrate the application of these models. Results indicate that a three-parameter logistic (3PL) model is sufficient to describe participants dichotomous responses (correct vs. incorrect) while persons’ ability parameters are quite robust across IRT models of varying complexity. These conclusions are in line with the original results of Myszkowski and Storme (2018). Using Bayesian as opposed to frequentist IRT models offered advantages in the estimation of more complex (i.e., 3–4PL) IRT models and provided more sensible and robust uncertainty estimates.

Inaccurate Individual Ability Estimates with Three-Parameter Item Response Models in Mixture Settings

ABSTRACTIt is demonstrated that the popular three-parameter logistic model can lead to markedly inaccurate individual ability level estimates for mixture populations. A theoretically and empirically important setting is initially considered where (a) in one of two subpopulations (latent classes) the two-parameter logistic model holds for each item in a measuring instrument, while (b) this model as well as the three-parameter logistic model for an item with guessing are valid for the instrument in the second class. Fitting the respective hybrid models then to the overall data set, with the three-parameter logistic model assumed for that item, is found to lead to notably inaccurate individual trait score estimates in either class. The implications of the reported results for contemporary empirical educational and behavioral research are finally discussed.

Large-scale Lassa fever outbreaks in Nigeria: quantifying the association between disease reproduction number and local rainfall.

Lassa fever (LF) is increasingly recognised as an important rodent-borne viral haemorrhagic fever presenting a severe public health threat to sub-Saharan West Africa. In 2017-18, LF caused an unprecedented epidemic in Nigeria and the situation was worsening in 2018-19. This work aims to study the epidemiological features of epidemics in different Nigerian regions and quantify the association between reproduction number (R) and state rainfall. We quantify the infectivity of LF by the reproduction numbers estimated from four different growth models: the Richards, three-parameter logistic, Gompertz and Weibull growth models. LF surveillance data are used to fit the growth models and estimate the Rs and epidemic turning points (τ) in different regions at different time periods. Cochran's Q test is further applied to test the spatial heterogeneity of the LF epidemics. A linear random-effect regression model is adopted to quantify the association between R and state rainfall with various lag terms. Our estimated Rs for 2017-18 (1.33 with 95% CI 1.29-1.37) was significantly higher than those for 2016-17 (1.23 with 95% CI: (1.22, 1.24)) and 2018-19 (ranged from 1.08 to 1.36). We report spatial heterogeneity in the Rs for epidemics in different Nigerian regions. We find that a one-unit (mm) increase in average monthly rainfall over the past 7 months could cause a 0.62% (95% CI 0.20%-1.05%)) rise in R. There is significant spatial heterogeneity in the LF epidemics in different Nigerian regions. We report clear evidence of rainfall impacts on LF epidemics in Nigeria and quantify the impact.

Use of Robust z in Detecting Unstable Items in Item Response Theory Models.

The first part of this paper describes the use of the robust zR statistic to link test forms using the Rasch (or one-parameter logistic) model. The procedure is then extended to the two-parameter and three-parameter logistic and two-parameter partial credit (2PPC) models. A real set of data was used to illustrate the extension. The linking results illustrate the efficacy of the robust zR vis-a-vis some of the most commonly used processes such as the Stocking and Lord (1983) linking process.

Marginalized maximum a posteriori estimation for the four-parameter logistic model under a mixture modelling framework.

The four-parameter logistic model (4PLM) has recently attracted much interest in various applications. Motivated by recent studies that re-express the four-parameter model as a mixture model with two levels of latent variables, this paper develops a new expectation-maximization (EM) algorithm for marginalized maximum a posteriori estimation of the 4PLM parameters. The mixture modelling framework of the 4PLM not only makes the proposed EM algorithm easier to implement in practice, but also provides a natural connection with popular cognitive diagnosis models. Simulation studies were conducted to show the good performance of the proposed estimation method and to investigate the impact of the additional upper asymptote parameter on the estimation of other parameters. Moreover, a real data set was analysed using the 4PLM to show its improved performance over the three-parameter logistic model.

Meta-Analytic and Economic Approaches for Evaluation of Pesticide Impact on Sclerotinia Stem Rot Control and Soybean Yield in the North Central United States.

As complete host resistance in soybean has not been achieved, Sclerotinia stem rot (SSR) caused by Sclerotinia sclerotiorum continues to be of major economic concern for farmers. Thus, chemical control remains a prevalent disease management strategy. Pesticide evaluations were conducted in Illinois, Iowa, Michigan, Minnesota, New Jersey, and Wisconsin from 2009 to 2016, for a total of 25 site-years (n = 2,057 plot-level data points). These studies were used in network meta-analyses to evaluate the impact of 10 popular pesticide active ingredients, and seven common application timings on SSR control and yield benefit, compared with not treating with a pesticide. Boscalid and picoxystrobin frequently offered the best reductions in disease severity and best yield benefit (P < 0.0001). Pesticide applications (one- or two-spray programs) made during the bloom period provided significant reductions in disease severity index (DIX) (P < 0.0001) and led to significant yield benefits (P = 0.0009). Data from these studies were also used in nonlinear regression analyses to determine the effect of DIX on soybean yield. A three-parameter logistic model was found to best describe soybean yield loss (pseudo-R2 = 0.309). In modern soybean cultivars, yield loss due to SSR does not occur until 20 to 25% DIX, and considerable yield loss (-697 kg ha-1 or -10 bu acre-1) is observed at 68% DIX. Further analyses identified several pesticides and programs that resulted in greater than 60% probability for return on investment under high disease levels.

The Bayesian Expectation-Maximization-Maximization for the 3PLM.

The current study proposes an alternative feasible Bayesian algorithm for the three-parameter logistic model (3PLM) from a mixture-modeling perspective, namely, the Bayesian Expectation-Maximization-Maximization (Bayesian EMM, or BEMM). As a new maximum likelihood estimation (MLE) alternative to the marginal MLE EM (MMLE/EM) for the 3PLM, the EMM can explore the likelihood function much better, but it might still suffer from the unidentifiability problem indicated by occasional extremely large item parameter estimates. Traditionally, this problem was remedied by the Bayesian approach which led to the Bayes modal estimation (BME) in IRT estimation. The current study attempts to mimic the Bayes modal estimation method and develop the BEMM which, as a combination of the EMM and the Bayesian approach, can bring in the benefits of the two methods. The study also devised a supplemented EM method to estimate the standard errors (SEs). A simulation study and two real data examples indicate that the BEMM can be more robust against the change in the priors than the Bayes modal estimation. The mixture modeling idea and this algorithm can be naturally extended to other IRT with guessing parameters and the four-parameter logistic models (4PLM).

A Note on the Presence of Spurious Pseudo-Guessing Parameters for Three-Parameter Logistic Models in Heterogeneous Populations

This note raises caution that a finding of a marked pseudo-guessing parameter for an item within a three-parameter item response model could be spurious in a population with substantial unobserved heterogeneity. A numerical example is presented wherein each of two classes the two-parameter logistic model is used to generate the data on a multi-item measuring instrument, while the three-parameter logistic model is found to be associated with a considerable pseudo-guessing parameter estimate on an item. The implications of the reported results for empirical educational research are subsequently discussed.

Multilevel Rasch Modeling: Does Misfit to the Rasch Model Impact the Regression Model?

Multilevel Rasch models are increasingly used to estimate the relationships between test scores and student and school factors. Response data were generated to follow one-, two-, and three-parameter logistic (1PL, 2PL, 3PL) models, but the Rasch model was used to estimate the latent regression parameters. When the response functions followed 2PL or 3PL models, the proportion of variance explained in test scores by the simulated student or school predictors was estimated accurately with a Rasch model. Proportion of variance within and between schools was also estimated accurately. The regression coefficients were misestimated unless they were rescaled out of logit units. However, item-level parameters, such as DIF effects, were biased when the Rasch model was violated, similar to single-level models.

A Graphical Method for Displaying the Model Fit of Item Response Theory Trace Lines.

Item response theory (IRT) is a statistical paradigm for developing educational tests and assessing students. IRT, however, currently lacks an established graphical method for examining model fit for the three-parameter logistic model, the most flexible and popular IRT model in educational testing. A method is presented here to do this. The graph, which is referred to herein as a "bin plot," is the IRT equivalent of a scatterplot for linear regression. Bin plots display a conventional IRT trace line (with ability on the horizontal axis and probability correct on the vertical axis). Students are binned according to how well they performed on the entire test, and the proportion of students in each bin who answered the focal question correctly is displayed on the graph as points above or below the trace line. With this arrangement, the difference between each point and the trace line is the residual for the bin. Confidence intervals can be added to the observed proportions in order to display uncertainty. Computer simulations were used to test four alternative ways for binning students. These simulations showed that binning students according to number of questions they answered correctly on the entire test works best. Simulations also showed confidence intervals for bin plots had coverage probabilities close to nominal values for common testing scenarios, but that there are scenarios in which confidence intervals had inflated error rates.