In presence of interval-censored data, we propose a general three-state disease model with covariates. Such data can arise, for example, in epidemiologic studies of infectious disease where both the times of infection...
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In this paper we describe a new method for the analysis of electron microscope autoradiographs. It uses a Poisson model to describe the autoradiographic grain distribution, and the method of maximum likelihood to esti...
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In this paper we describe a new method for the analysis of electron microscope autoradiographs. It uses a Poisson model to describe the autoradiographic grain distribution, and the method of maximum likelihood to estimate the radioactive intensities. An iterative procedure is derived from the em algorithm to produce maximum likelihood estimates. The procedure leads to simple iterative calculations and a complete treatment of edge effects. The resulting method of analysis enables data from the whole area of autoradiograph plates to be utilized without the need for any form of windowing to guard against edge effects. It also facilitates inference about the precision of estimated intensities and about comparisons between intensities. The estimation procedures are illustrated with real autoradiograph data from a study of rabbit blood plasma.
Let Y=(Y-t)(t greater than or equal to 0) be an unobserved random process which influences the distribution of a random variable T which can be interpreted as the time to failure. When a conditional hazard rate corres...
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Let Y=(Y-t)(t greater than or equal to 0) be an unobserved random process which influences the distribution of a random variable T which can be interpreted as the time to failure. When a conditional hazard rate corresponding to T is a quadratic function of covariates, Y, the marginal survival function may be represented by the first two moments of the conditional distribution of Y among survivors. Such a representation may not have an explicit parametric form. This makes it difficult to use standard maximum likelihood procedures to estimate parameters - especially for censored survival data. In this paper a generalization of the em algorithm for survival problems with unobserved, stochastically changing covariates is suggested. It is shown that, for a general model of the stochastic failure model, the smoothing estimates of the first two moments of Y are of a specific form which facilitates the em type calculations. Properties of the algorithm are discussed.
In this paper we study the maximum likelihood estimation of parameters, of the bivariate Poisson distribution, by assuming a sample with a general pattern of missing observations and applying the em algorithm (Dempste...
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In this paper we study the maximum likelihood estimation of parameters, of the bivariate Poisson distribution, by assuming a sample with a general pattern of missing observations and applying the em algorithm (Dempster, Laird and Rubin, 1977). The application of the method is outlined in the complete-data estimation problem, considered by Holgate (1964), since the latter can be viewed as a special case of the missing-value problem studied here. The observed information matrix is also obtained by means of the em algorithm (Louis, 1982) and numerical examples are presented. The application of Louis's method is found most appropriate and seen to produce remarkable acceleration in the convergence of the em algorithm. Results of some interest, concerning the conditional distributions of Poisson variables, given particular sums of Poisson random variables are also established.
Multinomial processing tree models assume that an observed behavior category can arise from one or more processing sequences represented as branches in a tree. These models form a subclass of parametric, multinomial m...
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Multinomial processing tree models assume that an observed behavior category can arise from one or more processing sequences represented as branches in a tree. These models form a subclass of parametric, multinomial models, and they provide a substantively motivated alternative to loglinear models. We consider the usual case where branch probabilities are products of nonnegative integer powers in the parameters, 0 less-than-or-equal-to theta(s) less-than-or-equal-to 1, and their complements, 1 - theta(s). A version of the em algorithm is constructed that has very strong properties. First, the E-step and the M-step are both analytic and computationally easy;therefore, a fast PC program can be constructed for obtaining MLEs for large numbers of parameters. Second, a closed form expression for the observed Fisher information matrix is obtained for the entire class. Third, it is proved that the algorithm necessarily converges to a local maximum, and this is a stronger result than for the exponential family as a whole. Fourth, we show how the algorithm can handle quite general hypothesis tests concerning restrictions on the model parameters. Fifth, we extend the algorithm to handle the Read and Cressie power divergence family of goodness-of-fit statistics. The paper includes an example to illustrate some of these results.
The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series. In these models the conditional distribution of the current observation given the past is a mixtur...
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The class of mixture transition distribution (MTD) time series models is extended to general non-Gaussian time series. In these models the conditional distribution of the current observation given the past is a mixture of conditional distributions given each one of the lastpobservations. They can capture non-Gaussian and nonlinear features such as flat stretches, bursts of activity, outliers changepoints in a single unified model class. They can also represent time series defined on arbitrary state spaces, univariate or multivariate, continuous, discrete or mixed, which need not even be Euclidean. They perform well in the usual case of Gaussian time series without obvious nonstandard behaviors. The models are simple, analytically tractable, easy to simulate readily estimated. The stationarity and autocorrelation properties of the models are derived. A simple em algorithm is given and shown to work well for estimation. The models are applied to several real and simulated datasets with satisfactory results. They appear to capture the features of the data better than the best competing autoregressive integrated moving average (ARIMA) models.
Models for fertility that take into account the timing of intercourse relative to ovulation are needed to estimate the influence of both endogenous and exogenous factors on human fertility. The classical model ,assume...
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Models for fertility that take into account the timing of intercourse relative to ovulation are needed to estimate the influence of both endogenous and exogenous factors on human fertility. The classical model ,assumes that some menstrual cycles are 'viable' and some are not, where 'viability' is determined by whether hormonal, uterine, and gamete-related factors are favorable to gestation. Within each viable cycle, the various days with intercourse are assumed to act independently, within each nonviable cycle, the days with intercourse can have no effect. Cycle viability for individual cycles is latent in that it is not ascertainable when conception does not occur. The classical model neglects the statistical dependency of outcomes among menstrual cycles within individual couples. Current marginal approaches cannot determine the degree to which heterogeneity in fecundability is biologically based versus the degree to which it is secondary to variation in intercourse behavior from couple to couple. We describe a random-effects model based on assuming that the cycle viability probability varies from couple to couple according to a beta distribution, and we use an em algorithm to fit the model. The proposed estimating procedure is fully expandable to allow covariate effects on the beta variate. Our method can be applied more generally whenever dependency among Bernoulli trials is induced by a susceptibility state and the outcomes can be observed only in the aggregate. Based on data from a cohort of couples with no known fertility problems who were attempting pregnancy, cycle viability is found to be heterogeneous among couples. Stratification on the presence or absence of prenatal exposure of the woman to her mother's cigarette smoking revealed a statistically significant difference in the two cycle viability distributions. We discuss differences in the interpretation of the beta model compared to the marginal approach based on generalized estimating equations. [ABSTR
Minimum Hellinger distance estimates are considered for finite mixture models when the exact forms of the component densities are unknown in detail but are thought to be close to members of some parametric family. Min...
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Minimum Hellinger distance estimates are considered for finite mixture models when the exact forms of the component densities are unknown in detail but are thought to be close to members of some parametric family. Minimum Hellinger distance estimates are asymptotically efficient if the data come from a member of the parametric family and are robust to certain departures from the parametric family. A new algorithm is introduced that is similar to the em algorithm, and a specialized adaptive density estimate is also introduced Standard measures of robustness are discussed, and some difficulties are noted. The robustness and asymptotic efficiency of the estimators are illustrated using simulations. [ABSTRACT FROM AUTHOR]
Monte Carlo methods were used to evaluate an em algorithm for correction for missing data in latent class analysis. Bias in parameter estimates was assessed under various assumptions concerning the mechanism for missi...
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Monte Carlo methods were used to evaluate an em algorithm for correction for missing data in latent class analysis. Bias in parameter estimates was assessed under various assumptions concerning the mechanism for missingness including cases where missingness was not at random. Findings suggest practical limits for the utility of the em algorithm in terms of sample size and nonresponse rate.
The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regim...
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The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between each directed pair of nodes, determined according to a known Markov chain fixed for that pair). Maximum likelihood estimation and related approximations are discussed, and computational difficulties are pointed out. A detailed methodology is presented for estimates based on the method of moments. The estimates are derived algorithmically, taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an em algorithm, resulting in a particularly simple solution to a hard problem. A small simulation study is carried out.
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