This work presents a new method for latent variable mixed models with missing data and extends the regression methods to obtain factor scores, as well as, letting covariates affect the latent variable directly. Maximum likelihood and least square methods are used to estimate model parameters and factor scores. The new model is applied to gross motor development data and the results are compared with two-stage factor analysis and structural equation models.

BACKGROUND AND OBJECTIVES: The classification of marine animals as protected species makes data and information on them to be very important. Therefore, this led to the need to retrieve and understand the data on the event counts for stranded marine animals based on location emergence, number of individuals, behavior, and threats to their presence. Whales are generally often stranded in very shallow areas with sloping sea floors and sand. Data were collected in this study on the incidence of stranded marine animals in 20 provinces of Indonesia from 2015 to 2019 with the focus on animals such as Balaenopteridae, Delphinidae, Lamnidae, Physeteridae, and Rhincodontidae. METHODS: Multivariate latent generalized linear model was used to compare several distributions to analyze the diversity of event counts. Two optimization models including Laplace and Variational approximations were also applied. FINDINGS: The best theta parameter in the latent multivariate latent generalized linear latent variable model was found in the Akaike Information Criterion, Akaike Information Criterion Corrected and Bayesian Information Criterion values, and the information obtained was used to create a spatial cluster. Moreover, there was a comprehensive discussion on ocean-atmosphere interaction and the reasons the animals were stranded. CONCLUSION: The changes in marine ecosystems due to climate change, pollution, overexploitation, changes in sea use, and the existence of invasive alien species deserve serious attention.

Background: A common way for computing test-retest reliability is Intra Class Correlation which was developed for continuous variables. But it widely used to assess test-retest reliability in questionnaires with Likert scales. Most of the time consecutive numbers regarded as option labels of a question. If the probability of choosing options be the same, using this method is logic, otherwise it is not. Therefore, in this study a modified estimator of ICC is proposed to improve the estimation of ICC for ordinal scale by using latent variable model. Method: In this method test-retest answers were considered as bivariate variables and cumulative Probit latent variable model was fitted. A simulation study with N=1500 replicates was conducted to compare the ICC estimations of Likert scale approach with a latent variable approach. Different sample sizes (n=20, 30) was generated with different correlation parameters. The simulations were repeated for questions with 3 and 5 options with different probability of selecting options of a question.  After that the two approaches were run on Beck for suicidal ideation questionnaire. Result: In general the difference between Likert scale approach and latent variable approach were higher in 3 question options compared to 5 and also by increasing sample size and correlation between bivariate data, Root Mean Square Errors and bias were decreased. Assuming different probabilities for options, there was a considerably difference between Root Mean Square Errors, bias and standard deviation of estimation of ICC in two models. Using latent variable approach resulted less bias, SD and Root Mean Square Errors especially in lower sample sizes. Conclusion: Simulations showed when the probability of choosing options of a question are skewed, using this method reduced Root Mean Square Errors especially when the options are less. This method was affected more on standard deviation compare to bias of estimations.

The present research aims to construct the latent variable of growth in Kermani sheep, and to evaluate the measurement model and genetic evaluation by applying pedigree and data information collected from 1993 to 2013 in the Breeding Station of Kermani sheep, Shahre Babak, Kerman Province. The records of body weights at birth (BWT), weaning (WWT), six months (SIXWT), nine months (NINEWT), and twelve months (YWT) of age were used to construct a growth latent variable. Fitting the measurement model considered for constructing the latent variable of growth was done by applying confirmatory factor analysis and was evaluated by using goodness of fit statistical measures including root mean square error of approximation (RMSEA), Tuker-Lewis index (TLI), and confirmatory fit index (CFI). The values of RMSEA, TLI, and CFI were obtained at 0.05, 0.99, and 0.99, respectively, implying the construct adequacy for assessing the latent variable of growth in Kermani sheep. An estimate of 0.34 was obtained for latent variable of growth. Positive estimates of genetic, phenotypic, and environmental correlations between the latent variable of growth and any of the investigated body weight traits were obtained. Furthermore, Spearman's rank correlations between estimated breeding values of the latent variable of growth with any of the investigated body weights were positive and high, implying the selection of superior animals for the latent variable of growth may result in the selection of superior animals for investigated body weights except for BWT.

Modeling correlated ordinal response data is usually more complex than the case of continuous and binary responses. Existing literature lacks an appropriate approach to modeling such data. For small sample sizes, however) these models lose their appeal since their inferences arc based OIl large samples. In this work, the Bayesian analysis of an asymmetric bivariate ordinal latent variable model has been developed. The latent response variable has been chosen to follow the generalized bivariate Gumble distribution. Using some specific priors and MCMC algorithms the regression parameters were estimated. As an application, a data set concerning Diabetic Retinopathy in 116 patients have been analyzed. This data set includes the disease status of each eye for patients as an ordinal response and a number of explanatory variables some of which are common to both eyes and the rest are organ specific.