mohsen mohammadzadeh

When discussing non-Gaussian spatially correlated variables, generalized linear mixed models have enough flexibility for modeling various data types. However, the maximum likelihood methods are plagued with substantial calculations for large data sets, resulting in long waiting times for estimating the model parameters. To alleviate this drawback, composite likelihood functions obtained from the product of the likelihoods of subsets of observations are used. The current paper uses the pairwise likelihood method to study the parameter estimations of spatial generalized linear mixed models. Then, we use the weighted pairwise and penalized likelihood functions to estimate the parameters of the mentioned models. The accuracy of estimates based on these likelihood functions is evaluated and compared with full likelihood function-based estimation using simulation studies. Based on our results, the penalized likelihood function improved parameter estimation. Prediction using penalized likelihood functions is applied. Ultimately, pairwise and penalized pairwise likelihood methods are applied to analyze count real data sets.

In this article, autoregressive spatial regression and second-order moving average will be presented to model the outputs of a heavy-tailed skewed spatial random field resulting from the developed multivariate generalized Skew-Laplace distribution. The model parameters are estimated by the maximum likelihood method using the Kolbeck-Leibler divergence criterion. Also, the best spatial predictor will be provided. Then, a simulation study is conducted to validate and evaluate the performance of the proposed model. The method is applied to analyze a real data.

Many survival data analyses aim to assess the effect of different risk factors on survival time‎. ‎In some studies‎, ‎the survival times are correlated‎, ‎and the dependence between survival times is related to their spatial locations‎. ‎Identifying and considering the dependence structure of data is essential in survival modeling‎. ‎The copula functions are helpful tools for incorporating data dependencies‎. ‎So‎, ‎one may use these functions for modelling spatial survival data‎. ‎This paper presents a model for spatial survival data by the Gumbel-Hougaard copula function‎. ‎A two-stage estimator using a composite likelihood function is used to estimate regression and dependence parameters‎. ‎A simulation study investigates the performance of the model‎. ‎Finally‎, ‎the proposed model is applied to model a set of COVID-19 data.

Models with spatial stochastic effects are commonly used to model the relationship between response variables and spatially dependent observations and explanatory variables. In many applications, some models' explanatory variables are dependent. Depending on the type of dependence, the statistical inference of the models with random effects and their applications are complicated; because the explanatory variables, random effects, and model error expression compete with each other in explaining the variability of the response variable.In this paper, a method for modeling and analyzing spatial survival data is proposed to solve this problem. Instead of using spatial stochastic effects in the model, the spatial dependence of observations is explicitly included in density, survival, and hazard functions. Then, in a simulation study, the effects of explanatory variables in the model are calculated and evaluated using the comparative Metropolis-Hastings algorithm. The proposed method is then used to analyze patients' data with prostate cancer, and the Bayesian approach is used to estimate the relative death risk of patients. Finally, a discussion and conclusion will be presented.

The present study was conducted for investigation the trend of soil carbon, total nitrogen and soil aggregate stability changes with increasing depth under different land uses in Alandan area–Sari. The soil samples were taken from soil depths 0-10, 10-20, 20-30, 30-40, 40-50 cm using coring (8 cm diameter) and auger method in each site systematic randomly (n=6). The soil texture, soil pH, the percentage of CaCO3, organic carbon, total nitrogen and geometric mean diameter (soil aggregate stability index) was measured in the laboratory. The result showed that, soil carbon and nitrogen were significantly (p<0.05) affected by soil depth and land use change. However, the geometric mean diameter was only affected by soil depth. The compared means showed that, the amount of carbon, nitrogen and soil aggregate stability index is significantly reduced with increasing soil depth. In the surface soil layers, the highest carbon (4.6%) and nitrogen (0.31%) were found in ash plantation and theirs lowest (2.5 % and 0.15% respectively) were observed in pine plantation. Also, soil organic carbon is significantly (p<0.05) increased with increasing geometric mean diameter.

Estimating the spatial hazard, or in other words, the probability of exceeding a certain boundary is one of the important issues in environmental studies that are used to control the level of pollution and prevent damage from natural disasters. Risk zoning provides useful information to decision-makers; For example, in areas where spatial hazards are high, zoning is used to design preventive policies to avoid adverse effects on the environment or harm to humans. Generally, the common spatial risk estimating methods are for stationary random fields. In addition, a parametric form is usually considered for the distribution and variogram of the random field. Whereas in practice, sometimes these assumptions are not realistic. For an example of these methods, we can point to the Indicator kriging, Disjunctive kriging, Geostatistical Markov Chain, and simple kriging.  In practice utilize the parametric spatial models caused unreliable results. In this paper, we use a nonparametric spatial model to estimate the unconditional probability or spatial risk:rcs0=PZs0⩾c.  (1) Because the conditional distribution at points close to the observations has less variability than the unconditional probability, nonparametric spatial methods will be used to estimate the unconditional probability.  

Let Z=Zs1,…,ZsnT be an observation vector from the random field {Zs;s∈D⊆Rd} which is decomposed as follows Zs=μs+εs,  (2) where μ(s) is the trend and ε(s) is the error term, that is a second-order stationary random field with zero mean and covariogram Ch=Covεs,εs+h. The local linear model for the trend is given by μHs= e1TSsTWsSs-1 SsTWsZ≡  ϕTsZ, where e1 is a vector with 1 in the first entry and all other entries 0, Ss is a matrix with ith row equal to (1, (si-s)T), Ws = diag {KHs1 – s,…,KH(sn-s)}, KHu=H-1K(H-1u), K is a triple multiplicative multivariate kernel function and H is a nonsingular symmetric d×d bandwidth matrix. In this model, the bandwidth matrix obtained from a bias corrected and estimated generalized cross-validation (CGCV). From nonparametric residuals ε(s) = Z(s) -μ(s) a local linear estimate of the variogram 2 γ(⋅)is obtained as the solution of the following least-squares problem minα.βi<jnεi-εj2-α-βT si-sj-u2 KGsi-sj-u, where G is the corresponding bandwidth matrix, that obtained from minimizing cross-validation relative squared error of semi-variogram estimate. Algorithm1: Semiparametric Bootstrap Obtain estimates of the error covariance and nonparametric residuals covariance. Generate bootstrap samples with the estimated spatial trend μHs and adding bootstrap errors generated as a spatially correlated set of errors. Compute the kriging prediction Z*s0 at each unsampled location s0 from the bootstrap sample Z*s1,…,Z*sn. Repeat steps 2 and 3 a larger number times B. Therefore, for each un-sampled location s0, B bootstrap replications Z*(1)s0.…. Z*(B)(s0) are obtained. Calculate (1) at position s_0 by calculating the relative frequency of Bootstrap repetition as follows to estimate the unconditional probability of excess of boundary c. rcs0= 1B j=1BIZ*js0≥ c

To analysis the practical behavior of the proposed methods a simulation study is conducted under different scenarios. For N=150 samples and n=16×16 were generated on a regular grid in the unit square following model (2), with mean function μs=2.5 + sin( 2π x1) + 4x2 - 0.5 2, and random errors normally distributed with zero mean and isotropic exponential covariogram  Ch= 0.04 + 2.01 1- exp-3 ∥ h∥0.5,   h∈ R2. For comparing nonparametric spatial methods for estimate unconditional risk, conditional risk, and Indicator kriging, we considered 7 missing observations in certain situations. Empirical spatial risk and its estimates are presented in Table 1. The Indicator kriging is overestimating and estimate spatial risk larger than 1. Generally, an estimated risk with unconditional and conditional methods is near value to empirical value. Table 1. Empirical spatial risk and its estimates Locations (0.13, 0) (0.87, 0.87) (0.80, 0.20) (0.94, 0.27) (0, 0.47) (074, .60) (0.34, 0.60) Methods 0.999 0.300 0.069 0.317 0.504 0.011 0.989 Empirical 0.998 0.351 0.054 0.347 0.494 0.057 0.954 Conditional 1.002 0.230 0.091 0.091 0.652 0.006 0.996 Indicator 1.000 0.388 0.418 0.481 0.602 0.024 0.994 Unconditional The spatial risk mapping for the maximum temperature means of Iran in 364 stations in March 2018 is obtained. By applying Algorithm 1 final trend and semi-variogram estimates are smoother than the pilot version.  The conditional and unconditional spatial risk with 150 bootstrap replicates for two values of threshold 25 and 31 on a 75×75 grid are estimated. The unconditional risk estimate is smoother than the conditional risk estimate. Because of this in the unconditional version, biased residual unused directly in the spatial prediction but in the conditional risk estimating, original residuals and simple kriging used.

The spatial risk estimated with the nonparametric spatial method. For the trend and variability of the random field, modeling applied a local linear nonparametric model. In the simulation study, this method better results than Indicator kriging. Because the flexibility of the nonparametric spatial method could apply for the construction of confidence or prediction intervals and hypothesis testing.

In modeling the variables related to each other, regression models are usually used assuming that the response variable is Normal. But in problems dealing with data such as the rate or ratio of an event distributed in the (0,1) interval, these models may provide out-of-range predictions for the response variable. In addition rate or ratio data are oftem asymmetrically distributed, and the use of symmetric distributions leads to invalid results. In such cases, the Beta regression model is used, in which the distribution of the response variable is in the Beta family. Bayesian analysis of these models generally requires the calculation of multiple integrals. The use of MCMC algorithms sometimes encounters long computation times and divergence. This work presents approximate methods for obtaining posterior distributions for Bayesian analysis of Beta regression models. Then the Integrated Nested Laplace Approximation will be offered for getting the posterior distributions in the Bayesian analysis of these models. Moreover, these models' application is illustrated on a real data set.

In spatio-temporal data analysis, the most common way to consider the spatio-temporal correlation structure of data is to use the covariance function, which is usually unknown and estimated based on observations. This method requires constraints such as stationarity, isotropy and separability for the random field. Although the acceptance of these hypotheses facilitates the fitting of valid models to the spatio-temporal covariance function, they are not necessarily realistic in applied problems. In this paper, to expedite the calculation of spatio-temporal prediction for a non-stationary and non-separable random field, a possible model based on spatial-temporal covariance tensor analysis based on Tucker analysis is investigated. Then, we show the proposed method for predicting wind energy based on spatio-temporal wind speed data at 31 weather stations in Iran.

In this paper, we define a spatial skew and heavy-tailed random field by an extended version of multivariate generalized skew Laplace distribution. The Bayesian spatial regression model is developed to explain the spatial data. A simulation study is then carried out to validate and evaluate the performance of the proposed model. The application of this model is also demonstrated in an analysis of a geological real data set.

In conventional methods for spatial survival data modeling, it is often assumed that the coefficients of explanatory variables in different regions have a constant effect on survival time. Usually, the spatial correlation of data through a random effect is also included in the model. But in many practical issues, the factors affecting survival time do not have the same effects in different regions. In this paper, we consider the spatial effects of factors affecting survival time are not the same in the different areas. For this purpose, spatial regression models and spatial varying coefficient models are introduced. Next, the Bayesian estimates of their parameters are presented. Three models of classical regression, spatial regression and spatial varying coefficient regression are used to analyze Esophageal cancer survival data. The relative risk of various factors is examined and evaluated.

Often, due to conditions under which measurements are made, spatio-temporal data contain missing values. Missing data in spatial or temporal vicinity may include useful information. Using this information, we can provide more accurate results, so missing data should be carefully examined. By modeling the missing process and spatio-temporal measurement process jointly, some lost information could be recovered. In this paper, we implement joint modeling in a Bayesian framework using the "shared parameter model" technique, so that the bad effects of missing values will be moderated. Also, we will associate these two processes via a latent spatio-temporal random field. To estimate the model parameters and for predictions, the Bayesian method INLA using SPDE approach is applied. Also, the lake surface water temperature data for Caspian sea is used to evaluate the performance of the joint model.

 Entry into the military service affects the mental health of individuals and one of the effective factors in mental health, especially in the current world, is the hope for a healthy life. The most important effect of hope is the improvement of motivation and activation. Hope is one of the variables that influence the happiness of people in society, especially the younger generation.

 The present study aimed at investigating the relationship of resilience and emotional regulation with life expectancy in soldiers.

 The present descriptive-correlational study was conducted in 2017 on 300 soldiers selected by convenience sampling method. The data collection instruments were the Conner and Davidson resiliency, the Gross and John emotional regulation, and the Miller life expectancy questionnaires. The reliability and validity of the questionnaires were confirmed in previous studies. In the current study, the reliability and validity of the instruments were determined using the Cronbach alpha coefficient, which were 0.89, 0.70, and 0.91, respectively. The collected data were analyzed using SPSS software version 20.

 The Pearson correlation coefficient showed the correlation of resilience and emotional regulation with soldiers' life expectancy (P <0.001). Resilience and emotional regulation had the potential for life expectancy in soldiers (P <0.05).
Discussion and

 The current study findings indicated a significant correlation of resilience and emotional regulation with life expectancy among soldiers. To increase the life expectancy in soldiers, the focused resilience training that increases the individual’s resistance to stress and emotion regulation that influences the individuals’ responses to different situations of life, especially in critical conditions, are essential.

The increase of heavy metals concentration in soils is potentially threatening the environment and human health. In this paper, multivariate analysis methods such as Positive Matrix Factorization (PMF), Principal Component Analysis (PCA) and Cluster Analysis (CA) combined with geostatistical method were employed to identify the potential sources of soil pollution. A collection of 103 samples were obtained from surface soils of different types of lithology and landuse in Zanjan Basin, Iran. The concentration of As, Bi, Cd, Co, Cr, Cu, Pb, Fe, Mo, Ni, Zn, Se and Hg beside of physical and chemical properties were measured. The results showed a strong effect of anthropogenic sources on the enrichment of heavy metals especially, Zn, Pb, Cd, As and Cu in soils. From the results of PMF and PCA, the four-factor model showed the optimized solution for this study. One of the factors is related to the background concentration, another one is associated with agricultural activities and the other two are associated with industrial activities and industrial waste. The PMF method in comparison with the other common methods in multivariate analysis presents physically acceptable and more reasonable results because of non-negative condition for factors and weighting of the variables.

Spatial statistics is the analytical science of spatial correlated data. In environmental fields of studies that deal with spatially correlated data due to their location in a given area, on the other hand, in the survey sampling it is assumed that the sample is taken from a population with independent units. This assumption is used at all stages of sampling, analysis and modeling. But when the units of the study population are correlated, the entire process, such as sampling methods and statistical process requires review and the entire process will be considering the correlation structure. In the classic sampling methods from a variable, when some covariates exist, then the balanced sampling is used for improving the quality of sample. In this paper, we introduce spatial balanced sampling design where the components of the spatial locations are considered as covariates. Then in an intensive simulation study Is shown that the kriging error induced by our sampling method is less than foe the other available methods. Finally, the application of the proposed method is shown in a real example.

‎One of the most useful tools for handling multivariate distributions of dependent variables in terms of their marginal distribution is a copula function‎. ‎The copula families capture a fair amount of attention due to their applicability and flexibility in describing the non-Gaussian spatial dependent data‎. ‎The particular properties of the spatial copula are rarely seen in all the known copula families‎. ‎In the present paper‎, ‎based on‎ ‎the weighted geometric mean of two Max-id copulas family‎, ‎the spatial copula function is provided‎. ‎Afterwards‎, ‎the proposed copula‎ ‎along with the Bees algorithm is used to explore the spatial dependency and to interpolate the rainfall data in Iranchr('39')s Khuzestan province‎.

Spatial generalized linear mixed models are used commonly for modelling non-Gaussian discrete spatial responses. We present an algorithm for parameter estimation of the models using Laplace approximation of likelihood function. In these models, the spatial correlation structure of data is carried out by random effects or latent variables. In most spatial analysis, it is assumed that random effects have Gaussian distribution, but the assumption is questionable. This assumption is replaced in the present work, using a skew Gaussian distribution for the latent variables, which is more flexible and includes Gaussian distribution. We examine the proposed method using a real discrete data set.

The strong correlation between vascular calcification and cardiovascular risk, which is a major cause of mortality in hemodialysis (HD) patients, has been well established. Fetuin-A is an inhibitor of vascular calcification, and pentraxin 3 (PTX3) is produced at the site of inflammation, which is associated with cardiovascular disease (CVD). The main purpose of this study was evaluating the correlation between fetuin-A and PTX3with some biochemical parameters effective upon vascular calcification in HD patients.
We included 84 HD patients and 84 healthy controls matched for age, gender, and body mass index (BMI) in this study. Blood samples were drawn from all subjects and the serum levels of creatinine, urea, albumin, calcium (Ca), phosphorus (P), lowdensity lipoprotein cholesterol (LDL-C), parathyroid hormone, fetuin-A, high sensitive C-reactive protein, and PTX3were measured by biochemical methods.
We found that the serum levels of PTX3, C-reactive protein (CRP), parathyroid hormone (PTH), Ca, and P in the patient group were significantly higher than the control group but the serum levels of fetuin-A and albumin were significantly lower in the patient group. Also, fetuin-A had a significant correlation with high sensitive CRP (hs-CRP) as well as duration of dialysis. In addition, it was shown that the correlation between PTX3 and PTH was significant only in the patient group.
In this study, increased PTX3 and decreased fetuin-A levels were observed in the HD patients. According to our results, these 2 parameters may potentially serve as suitable markers for inflammation and prediction of vascular complications in these patients.

Many studies in different areas include data in the form of rates or proportions that should be analyzed. The data may also accept values zero and one. Augmented beta regression models are an appropriate choice for continuous response variables in the closed unit interval [0,1]. The data in this model are based on a combination of three distributions, degenerate distribution at 0 and 1, and a beta density in (0,1). The random effects are usually added to the model for accommodating the data structures as well as correlation impacts. In most of these models, the random effects are generally assumed to be normally distributed, while this assumption is frequently violated in applied studies. In this paper, the augmented mixed beta regression model with skew-normal distributed random effects is presented. A Bayesian approach is adopted for parameter estimation using Markov Chain Monte Carlo method. The proposed model is applied to analyze a real data set from Labor Force Survey.

The Beta regression model is usually used for modeling the rates or proportions confined in an open interval (0,1). In some studies, the data may also include zero and one. In this paper, an augmented Beta regression model that is a mixture of Beta distribution with two degenerated distributions at 0 and 1 is presented for rates or proportions confined in [0,1]. For the augmented mixed Beta model with reparametrization of Beta distribution, the mean and precision parameters were modeled including fixed and random effects. This is while taking into account that the random effects make these models applicable to correlated data. Here, the augmented mixed Beta model is presented. Then this model is evaluated in a simulation study. Next, the application of this model is shown for analyzing the proportions of employed persons in every household. Finally, conclusion and results are presented.

Direct estimators of parameters are not precise because of little surveys unit in small areas. Regarding the wide spread increase of demand for providing valid and accurate statistics for small areas, attempts have been made to present proper solutions for the problems. Small area estimation approaches provide the direct estimators with borrowing strength to increase their precision based on a model, especially about those estimators that are based on the linear mixed model including random area effects and using various auxiliary sources. Data associated with spatially contiguous small areas may be modeled via covariates, with error terms that are spatially dependent according to neighbor areas. In this paper we investigate small area estimation based on linear models with spatially correlated small area effects where the neighborhood structure is described by a contiguity matrix. Such models allow efficient use of spatial auxiliary information in small area estimation. Then estimation for small areas will be achieved for the amount of agronomy production in Fars province, according to the two common EBLUP and MBDE methods and two usual (non spatial) and spatial approaches based on the unit level model. Then the accuracy of them have been compared.

ýBy existing censor and skewness in survival dataý, ýsome models such as weibull are used to analyzing survival dataý.
ýIn addition, parametric and semiparametric models can be obtained from baseline hazard function of Cox model to fit to survival dataý. ýHowever these models are popular because of their simple usage but do not consider unknown risk factorsý, ýthat's why cannot introduce the best fit to the data necessarilyý.
ýIn this paper by considering multiple random effects in Cox modelý, ýfrailty models are introducedý. ýThen using presented modelsý, ýesophageal cancer data in Golestan were modeled and fitted models were evaluated and compared based on generalized coefficient of determination criterioný.

One of the most widely used models for fitting survival data is Cox proportional hazards model that is based on homogeneity, independence and equi-distributed of survival data. But in many cases hazards of statistical units are different and the assumption of population homogeneity is not established. One of the reasons for such deference is the unknown or unobserved risk factors which may lead to some misleading models if there is no concern for them or some models such as Cox proportional hazard models have to be implemented. In such cases, regarding the unknown risk factors, frailty models are used. In this paper the performances of the Cox and frailty models for survival and spatial survival data with unknown risk factors are considered. The efficiency of these models whilst the source of unknown risk factors is the spatial correlation of survival data is also examined.

Non-Gaussian spatial responses are usually modeled using spatial generalized linear mixed models، such that the spatial correlation of the data can be introduced via normal latent variables. The model parameters and the prediction of the latent variables at unsampled locations are of the most important interest in SGLMM by estimating of the latent variables at sampled locations. In these models، since there are the latent variables and non-Gaussian spatial response variables، likelihood function cannot usually be given in a closed form and maximum likelihood estimations may be computationally prohibitive. In this paper، a new algorithm is introduced for maximum likelihood estimation of the model parameters and predictions، that is faster than the former method. This algorithm obtains to combine the pseudo maximum likelihood method، the Expectation maximization Gradient algorithm and an approximate method. The performance and accuracy of the proposed model are illustrated through a simulation study. Finally، the model and the algorithm are applied to a case study on rainfall data observed in the weather stations of Semnan in 2012.