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1.
This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as well as sample reallocation to latent classes. The results show that the clarity of remaining latent classes, as measured by the entropy statistic depends on the number of observations in the omitted latent class—but this statistic is not reliable. Specification error in the latent Markov model focuses on the transition probabilities when a longitudinal Guttman process is incorrectly specified. The findings show that specifying a longitudinal Guttman process that is not true in the population impacts other transition probabilities through the covariance matrix of the logit parameters used to calculate those probabilities. 相似文献
2.
Semicontinuous variable analysis is a widely appreciated statistical method in such disciplines as social science, medicines, and economics. In detecting underlying structure and representing possible interrelationships, statistical analysis using a two-part model is appropriated. In this paper, we present a general extension of two-part model to the situation where the unobserved factors are included in the two parts to interpret external variability in semicontinuous variable. Auxiliary information on these factors is manifested by continuous responses via measurement model, while the interrelationships among factors are exploited through structural equation model. Moreover, under longitudinal setting, dynamic characteristics of responses between any two occasions are represented by transition model. Procedures for model fitting, parameter estimation, model selection and prediction are developed within the Bayesian paradigm. Markov Chains Monte Carlo method is used to implement posterior analysis. Empirical results including a simulation and a real example are used to illustrate the proposed methodology. 相似文献
3.
In psychological, social, behavioral, and medical studies, hidden Markov models (HMMs) have been extensively applied to the simultaneous modeling of heterogeneous observation and hidden transition in the analysis of longitudinal data. However, the majority of the existing HMMs are developed in a parametric framework without latent variables. This study considers a novel semiparametric HMM, which comprises a semiparametric latent variable model to investigate the complex interrelationships among latent variables and a nonparametric transition model to examine the linear and nonlinear effects of potential predictors on hidden transition. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the unknown, a Bayesian model comparison statistic, is employed to conduct model comparison. The empirical performance of the proposed methodology is evaluated through simulation studies. An application to a data set derived from the National Longitudinal Survey of Youth is presented. 相似文献
4.
唐玉玲 《株洲师范高等专科学校学报》2007,12(5):36-38
根据随机过程原理与生命科学模型。简单的就业问题可以看作是具有两个瞬态的Markov过程．通过对就业转移概率、失业转移概率以及期望逗留期与就业强度和失业强度关系的研究，结果表明：就业转移概率和期望逗留期与就业强度具有相同的增减性。失业转移概率与失业强度的增减性则正好相反． 相似文献
5.
基于马尔可夫链的一类学习效率预测模型 总被引：1，自引：0，他引：1
本文利用马尔可夫链理论,在教学条件基本稳定不变的前提下,构建学生学习状态转移概率矩阵,用极限概率预测学生今后的学习状态,运用条件数学期望分析学习状态转变对学习效率的影响,建立预测远期学习效率的数学模型。 相似文献
6.
Herbert W. Marsh 《Journal of Educational Measurement》1993,30(2):157-183
The purpose of this investigation is to evaluate structural equation models (SEMs) for measures of the same construct collected on multiple occasions (one-variable, multiwave panel studies). Simplex models hypothesize that a measure at any one wave is substantially influenced by the measure at the 0immediately preceding wave; correlations between the same construct measured on different occasions are predicted to decline systematically as the number of intervening occasions increases. Alternatively, a one-factor model posits that a person's score at any one time is a function of some underlying "true" score and a random disturbance that is idiosyncratic to the time; no temporal ordering of correlations is assumed. Both the simplex and one-factor models can befit when there is only a single indicator of each construct at each wave (e.g., scale scores), but there are serious limitations to such models. Stronger models are possible when the same set of multiple indicators (e.g., the items that make up the scale) is measured at each wave. In Study 1, based on students' evaluations of teaching effectiveness collected over an 8-year period, one-factor models fit the data well, whereas simplex models did not. In Study 2, based on personality variables collected over a 4-year period during adolescence, one-factor models again provided an excellent fit to the data, whereas the simplex model did marginally poorer. The results challenge an overreliance on simplex models and demonstrate that a one-factor model is a potentially useful alternative that should be considered in multiwave studies. 相似文献
7.
Roberto Di Mari Daniel L. Oberski Jeroen K. Vermunt 《Structural equation modeling》2016,23(5):649-660
Latent Markov models with covariates can be estimated via 1-step maximum likelihood. However, this 1-step approach has various disadvantages, such as that the inclusion of covariates in the model might alter the formation of the latent states and that parameter estimation could become infeasible with large numbers of time points, responses, and covariates. This is why researchers typically prefer performing the analysis in a stepwise manner; that is, they first construct the measurement model, then obtain the latent state classifications, and subsequently study the relationship between covariates and latent state memberships. However, such a stepwise approach yields downward-biased estimates of the covariate effects on initial state and transition probabilities. This article, shows how to overcome this problem using a generalization of the bias-corrected 3-step estimation method proposed for latent class analysis (Asparouhov & Muthén, 2014; Bolck, Croon, & Hagenaars, 2004; Vermunt, 2010). We give a formal derivation of the generalization to latent Markov models and discuss how it can be used with many time points by incorporating it into a Baum–Welch type of expectation-maximization algorithm. We evaluate the method through a simulation study and illustrate it using an application on household financial portfolio change. Our study shows that the proposed correction method yields unbiased parameter estimates and accurate standard errors, except for situations with very poorly separated classes and a small sample. 相似文献
8.
林添华 《安顺师范高等专科学校学报》2009,11(3):90-92
马尔可夫公式是一种特殊的概率模式。其研究对象为一个运行系统的状态和状态转移。由于许多经济系统的动态过程可以抽象成状态转移过程,所以应用马尔可夫链方法研究一个运行系统的状态和状态转移,在经济生活中有着非常广泛的应用前景。在利用马尔可夫链进行市场预测时,其关键是状态转移概率的确定。 相似文献
9.
《Structural equation modeling》2013,20(3):369-389
The classic approach for partitioning and assessing reliability and validity has been through the use of the multitrait-multimethod (MTMM) model. The MTMM approach generally involves 3 different groups (method) evaluating 3 traits. This approach can be reconceptualized for questionnaire evaluation, so that the method becomes 3 different scaling types, which are administered to the same respondents on different occasions to avoid carryover effects. A serious limitation of this MTMM model is that data are required from respondents on at least 3 different occasions, thus placing a heavy burden on the researcher and respondents. Planned incomplete data designs for the purpose of substantially reducing the amount of data required for MTMM models were investigated: 1st, a design that reduces the amount of data collected at the 3rd administration by 22%; and 2nd, a design in which data need only be collected at 2 occasions. The performance of Listwise Deletion, Pairwise Deletion, and the expectation maximization (EM) algorithm at dealing with planned incomplete data are examined through a series of simulations. Results indicate that EM was generally precise and efficient. 相似文献
10.
在混合模型的观点下,状态转移模型形成具有后验权重的混合模型,它通过后验概率推测分布来源,再结合Markov转移概率矩阵实现对分布持续性的刻画,从而弥补固定权重混合模型在时变性和相关性方面的缺陷.文章得到了该模型下随机变量的条件分布和无条件分布的递推式,从而得到条件与无条件期望、方差,进一步研究了平稳性条件,揭示了模型二阶矩的相关性.最后通过实例展示了Markov后验权重混合模型的优越性和对"波动聚集"的捕捉能力. 相似文献
11.
马尔可夫预测方法在预测领域有着广泛的应用．该方法应用的一个重要的问题就是如何估计一步状态转移概率矩阵．在历史资料没有给出系统处于n个状态次数的情况下，给出一步状态转移概率矩阵估计的最优化方法．最后探讨了基于Markov链的最优化预测模型在长江水质预测中的应用，从而表明该模型的有效性． 相似文献
12.
刘家有 《合肥联合大学学报》2006,16(2):15-18
研究了带马尔科夫链利率的完全离散时间风险模型的有限时间和最终时间破产概率,给出了破产概率的递归方程和积分方程.当利率非负时,用鞅方法给出了推广的最终时间破产概率的Lundberg不等式. 相似文献
13.
CHANG Hong RU Feng XUE Jun-yi 《重庆大学学报(英文版)》2006,5(4):205-211
1 Introduction a After many years’ research and developments, communication networks have demonstrated more and more important functions in a substation automation system (SAS). In our experience in developing and applying such systems, we have witnessed… 相似文献
14.
This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps: (1) use GM (1,1) to fit the trend of the data, and obtain the relative error of the fitted values; (2) divide the relative error into ‘state’ data based on pre-set intervals; (3) calibrate the weighted Markov chain model: herein the parameters are the pre-set interval and the step of transition matrix (TM); (4) by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, (5) validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval (DAI) is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data. 相似文献
15.
In traditional Bayesian software reliability models, it was assume that all probabilities are precise. In practical applications
the parameters of the probability distributions are often under uncertainty due to strong dependence on subjective information
of experts’ judgments on sparse statistical data. In this paper, a quasi-Bayesian software reliability model using interval-valued
probabilities to clearly quantify experts’ prior beliefs on possible intervals of the parameters of the probability distributions
is presented. The model integrates experts’ judgments with statistical data to obtain more convincible assessments of software
reliability with small samples. For some actual data sets, the presented model yields better predictions than the Jelinski-Moranda
(JM) model using maximum likelihood (ML).
Project supported by the National High-Technology Research and Development Program of China (Grant Nos.2006AA01Z187, 2007AA040605) 相似文献
16.
《Structural equation modeling》2013,20(4):621-636
In applications of structural equation modeling, it is often desirable to obtain measures of uncertainty for special functions of model parameters. This article provides a didactic discussion of how a method widely used in applied statistics can be employed for approximate standard error and confidence interval evaluation of such functions. The described approach is illustrated with data from a cognitive intervention study, in which it is used to estimate time-invariant reliability in multiwave, multiple indicator models. 相似文献
17.
James A. Fitzgerald 《Journal of Experimental Education》2013,81(4):364-367
Many mechanistic rules of thumb for evaluating the goodness of fit of structural equation models (SEM) emphasize model parsimony; all other things being equal, a simpler, more parsimonious model with fewer estimated parameters is better than a more complex model Although this is usually good advice, in the present article a heuristic counterexample is demonstrated in which parsimony as typically operationalized in indices of fit may be undesirable. Specifically, in simplex models of longitudinal data, the failure to include correlated uniquenesses relating the same indicators administered on different occasions will typically lead to systematically inflated estimates of stability. Although simplex models with correlated uniquenesses are substantially less parsimonious and may be unacceptable according to mechanistic decision rules that penalize model complexity, it can be argued a priori that these additional parameter estimates should be included. Simulated data . are used to support this claim and to evaluate the behavior of a variety of fit indices and decision rules. The results demonstrate the validity of Bollen and Long’s (1993) conclusion that “test statistics and fit indices are very beneficial, but they are no replacement for sound judgment and substantive expertise” (p. 8). 相似文献
18.
以一型号火车车轮为例，综合考虑其加工要求，研究其数控加工模型的建模方法：提出了用逐步追加扩展数据段将工艺过程模型和生产工具模型集成到产品模型的渐进式建模方法，并采用十字链表结构的图形数据库存储方法。该建模方法包含了数控编程所需的信息。 相似文献
19.
Kristina R. Cassiday Youngmi Cho Jeffrey R. Harring 《Educational and psychological measurement》2021,81(4):668
Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth mixture model is used in this simulation study, and the design crosses three manipulated variables—number of latent classes, latent class probabilities, and class separation, yielding a total of 18 conditions. Within each of these conditions, the accuracy of a priori identifiability constraints, a priori training of the algorithm, and four post hoc algorithms developed by Tueller et al.; Cho; Stephens; and Rodriguez and Walker are tested to determine their classification accuracy. Findings reveal that, of all a priori methods, training of the algorithm leads to the most accurate classification under all conditions. In a case where an a priori algorithm is not selected, Rodriguez and Walker’s algorithm is an excellent choice if interested specifically in aggregating class output without consideration as to whether the classes are accurately ordered. Using any of the post hoc algorithms tested yields improvement over baseline accuracy and is most effective under two-class models when class separation is high. This study found that if the class constraint algorithm was used a priori, it should be combined with a post hoc algorithm for accurate classification. 相似文献
20.
The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random‐effect approach to allow examinees to have different probabilities of slipping and guessing. Two extensions of the DINA model were developed and tested to represent the random components of slipping and guessing. The first model assumed that a random variable can be incorporated in the slipping parameters to allow examinees to have different levels of caution. The second model assumed that the examinees’ ability may increase the probability of a correct response if they have not mastered all of the required attributes of an item. The results of a series of simulations based on Markov chain Monte Carlo methods showed that the model parameters and attribute‐mastery profiles can be recovered relatively accurately from the generating models and that neglect of the random effects produces biases in parameter estimation. Finally, a fraction subtraction test was used as an empirical example to demonstrate the application of the new models. 相似文献