scholarly journals AN ALTERNATIVE TO CLASSICAL LATENT CLASS MODELS SELECTION METHODS FOR SPARSE BINARY DATA: AN ILLUSTRATION WITH SIMULATED DATA

2017 ◽  
Vol 23 (1) ◽  
pp. 199-220
Author(s):  
Carlomagno Araya Alpizar
Keyword(s):  
Binary Data ◽  
Goodness Of Fit ◽  
Latent Class ◽  
Empirical Distribution ◽  
Latent Class Model ◽  
Simulated Data ◽  
Latent Class Models ◽  
Type I ◽  
Chi Square ◽  
Goodness Of Fit Tests

Within the context of a latent class model with manifest binary variables, we propose an alternative method that solves the problem of estimating empirical distribution with sparse contingency tables and the chi-square approximation for goodness-of-fit will not be valid. We analyze sparse binary data, where there are many response patterns with very small expected frequencies in several data sets varying in degree of sparseness from 1 to 5 defined d = n/2p = n/R is a factor that is mentioned in almost all prior literature as being an important determinant of how well the distribution is represented by the chi-squared.The proposed approach produced results that were valid and reliable under the mentioned problematic data conditions. Results from the proposal presented compare the rates of Type I for traditional goodness-of-fit tests. We also show that with data density d ≤ 5, Pearson’s statistic

scholarly journals Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data

2020 ◽  
Vol 8 (3) ◽  
pp. 30 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Latent Class ◽  
Latent Class Model ◽  
Simulated Data ◽  
Latent Class Models ◽  
Latent Classes ◽  
Polytomous Item ◽  
Item Functioning ◽  
Item Responses ◽  
Polytomous Item Responses ◽  
Raven's Standard Progressive Matrices

The last series of Raven’s standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization for RLCMs is proposed. For polytomous item responses, different alternative fused regularization penalties are presented. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes. In total, three out of five latent classes are ordered for all items. For the remaining two classes, violations for two and three items were found, respectively, which can be interpreted as a kind of latent differential item functioning.

Quantifying annual patterns in the frequency of mammalian births: do goodness-of-fit tests provide adequate inferences?

2012 ◽  
Vol 60 (6) ◽  
pp. 381 ◽  
Author(s):  
Evan Watkins ◽  
Julian Di Stefano
Keyword(s):  
Sample Size ◽  
Effect Size ◽  
Statistical Power ◽  
Goodness Of Fit ◽  
A Priori ◽  
Simulated Data ◽  
Maximum Effect ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Power Studies

Hypotheses relating to the annual frequency distribution of mammalian births are commonly tested using a goodness-of-fit procedure. Several interacting factors influence the statistical power of these tests, but no power studies have been conducted using scenarios derived from biological hypotheses. Corresponding to theories relating reproductive output to seasonal resource fluctuation, we simulated data reflecting a winter reduction in birth frequency to test the effect of four factors (sample size, maximum effect size, the temporal pattern of response and the number of categories used for analysis) on the power of three goodness-of-fit procedures – the G and Chi-square tests and Watson’s U2 test. Analyses resulting in high power all had a large maximum effect size (60%) and were associated with a sample size of 200 on most occasions. The G-test was the most powerful when data were analysed using two temporal categories (winter and other) while Watson’s U2 test achieved the highest power when 12 monthly categories were used. Overall, the power of most modelled scenarios was low. Consequently, we recommend using power analysis as a research planning tool, and have provided a spreadsheet enabling a priori power calculations for the three tests considered.

scholarly journals Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data

2020 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Latent Class Analysis ◽  
Latent Class ◽  
Latent Class Model ◽  
Simulated Data ◽  
Latent Class Models ◽  
Class Analysis ◽  
Polytomous Item ◽  
Item Responses ◽  
Polytomous Item Responses ◽  
Raven's Standard Progressive Matrices

The last series of Raven's standard progressive matrices (SPM-LS) test were studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCM). For dichotomous item response data, an alternative estimation approach for RLCMs is proposed. For polytomous item responses, different alternatives for performing regularized latent class analysis are proposed. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes.

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

Inheritance and linkage of isozymes in Populus tremuloides (Michx.)

Genome ◽  
1987 ◽  
Vol 29 (2) ◽  
pp. 384-388 ◽  
Author(s):  
Jung O. Hyun ◽  
Om P. Rajora ◽  
Louis Zsuffa
Keyword(s):  
Populus Tremuloides ◽  
Goodness Of Fit ◽  
Single Gene ◽  
Gene Control ◽  
Glutamate Oxaloacetate Transaminase ◽  
Chi Square ◽  
Banding Patterns ◽  
Phosphogluconate Dehydrogenase ◽  
Goodness Of Fit Tests ◽  
Populus Species

Progenies of four controlled crosses were assayed electrophoretically to determine the inheritance of isozymes of 10 loci coding for six enzymes, aconitase (ACO), glutamate oxaloacetate transaminase (GOT), isocitrate dehydrogenase (IDH), phosphoglucomutase (PGM), 6-phosphogluconate dehydrogenase (6-PGD), and phosphoglucose isomerase (PGI), in roots of Populus tremuloides. Chi-square goodness of fit tests verified a single-gene Mendelian control of the segregating allozyme variants at each of five loci: Aco-1, Got, Pgm-2, 6-Pgd-2, and Pgi-2. Evidence was also obtained for a single-gene control of each of the remaining five loci (Aco-2, Idh, Pgm-1, 6-Pgd-1, and Pgi-1). ACO and PGM showed monomeric, while GOT, IDH, 6-PGD, and PGI had dimeric, banding patterns. The results of joint two-locus segregation tests indicated no linkage between 6-Pgd-2 and Pgi-2. Key words: Populus species, electrophoresis, allozymes, inheritance, linkage.

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