Estimating a boundary line model for a biological response by maximum likelihood

The boundary line model was proposed to interpret biological data sets, where one variable is a biological response (e.g. crop yield) to an independent variable (e.g. available water content of the soil). The upper (or lower) boundary on a plot of the dependent variable (ordinate) against the independent variable (abscissa) represents the limiting response of the dependent variable to the independent variable value. Although the concept has been widely used, the methods proposed to define the boundary line have been subject to criticism. This is because of their ad hoc nature and lack of theoretical basis. In this article, we present a novel method for fitting the boundary line to a set of data. The method uses a censored probability distribution to interpret the data structure. The parameters of the distribution (and hence the boundary line parameters) are fitted using maximum likelihood and related confidence intervals deduced. The method is demonstrated using both simulated and real data sets.     

Application of pattern-mixture models to outcomes that are potentially missing not at random using pseudo maximum likelihood estimation

In this work, we fit pattern-mixture models to data sets with responses that are potentially missing not at random (MNAR, Little and Rubin, 1987). In estimating the regression parameters that are identifiable, we use the pseudo maximum likelihood method based on exponential families. This procedure provides consistent estimators when the mean structure is correctly specified for each pattern, with further information on the variance structure giving an efficient estimator. The proposed method can be used to handle a variety of continuous and discrete outcomes. A test built on this approach is also developed for model simplification in order to improve efficiency. Simulations are carried out to compare the proposed estimation procedure with other methods. In combination with sensitivity analysis, our approach can be used to fit parsimonious semi-parametric pattern-mixture models to outcomes that are potentially MNAR. We apply the proposed method to an epidemiologic cohort study to examine cognition decline among elderly.     

Maximum likelihood outperforms maximum parsimony even when evolutionary rates are heterotachous

Heterotachy occurs when the relative evolutionary rates among sites are not the same across lineages. Sequence alignments are likely to exhibit heterotachy with varying severity because the intensity of purifying selection and adaptive forces at a given amino acid or DNA sequence position is unlikely to be the same in different species. In a recent study, the influence of heterotachy on the performance of different phylogenetic methods was examined using computer simulation for a four-species phylogeny. Maximum parsimony (MP) was reported to generally outperform maximum likelihood (ML). However, our comparisons of MP and ML methods using the methods and evaluation criteria employed in that study, but considering the possible range of proportions of sites involved in heterotachy, contradict their findings and indicate that, in fact, ML is significantly superior to MP even under heterotachy.     

Maximum likelihood estimation of ordered multinomial parameters

The pool adjacent violator algorithm Ayer et al. (1955, The Annals of Mathematical Statistics, 26, 641-647) has long been known to give the maximum likelihood estimator of a series of ordered binomial parameters, based on an independent observation from each distribution (see Barlow et al., 1972, Statistical Inference under Order Restrictions, Wiley, New York). This result has immediate application to estimation of a survival distribution based on current survival status at a set of monitoring times. This paper considers an extended problem of maximum likelihood estimation of a series of 'ordered' multinomial parameters p(i)= (p(1i),p(2i),.,p(mi)) for 1 相似文献   

On maximum likelihood solutions for exponential survival models

"Stochastic survival models which adjust for covariate information have been developed by Beck (1979). These models can include one or two living states and several competing death states. The transitions between stages are assumed irreversible and the transition intensity functions are assumed to be independent of time but dependent upon the covariates." Explicit solutions of the maximum likelihood equations for such models when there are one or two dichotomous covariates are presented. Applications of these models to the case of heart transplants and lung cancer are discussed, and survival in two or four groups is compared. (summary in FRE)     

Approximate maximum likelihood estimation for logistic regression with covariate measurement error

In nutritional epidemiology, dietary intake assessed with a food frequency questionnaire is prone to measurement error. Ignoring the measurement error in covariates causes estimates to be biased and leads to a loss of power. In this paper, we consider an additive error model according to the characteristics of the European Prospective Investigation into Cancer and Nutrition (EPIC)‐InterAct Study data, and derive an approximate maximum likelihood estimation (AMLE) for covariates with measurement error under logistic regression. This method can be regarded as an adjusted version of regression calibration and can provide an approximate consistent estimator. Asymptotic normality of this estimator is established under regularity conditions, and simulation studies are conducted to empirically examine the finite sample performance of the proposed method. We apply AMLE to deal with measurement errors in some interested nutrients of the EPIC‐InterAct Study under a sensitivity analysis framework.     

A nonparametrie maximum likelihood estimator for incomplete renewal data

The problem of estimating the lifetime distribution based ondata from independently and identically distributed stationaryrenewal processes is addressed. The data are incomplete. A nonparametricmaximum likelihood estimate of the Lifetime distribution isderived using the em algorithm. The missing information principleis used to estimate the standard error of the estimated distribution.The methodology is applied to a problem in the nursing professionwhere nurses withdraw from active service for a period of timebefore returning to take up post at a later date. It is importantthat nurse manpower planners accurately predict this patternof return. The data analysed are from the Northern Ireland nursingprofession.     

IV estimation without distributional assumptions

It is widely known that Instrumental Variable (IV) estimation allows the researcher to estimate causal effects between an exposure and an outcome even in face of serious uncontrolled confounding. The key requirement for IV estimation is the existence of a variable, the instrument, which only affects the outcome through its effects on the exposure and that the instrument–outcome relationship is unconfounded. Countless papers have employed such techniques and carefully addressed the validity of the IV assumption just mentioned. However, less appreciated is that fact that the IV estimation also depends on a number of distributional assumptions in particular linearities. In this paper, we propose a novel bounding procedure which can bound the true causal effect relying only on the key IV assumption and not on any distributional assumptions. For a purely binary case (instrument, exposure, and outcome all binary), such boundaries have been proposed by Balke and Pearl in 1997. We extend such boundaries to non-binary settings. In addition, our procedure offers a tuning parameter such that one can go from the traditional IV analysis, which provides a point estimate, to a completely unrestricted bound and anything in between. Subject matter knowledge can be used when setting the tuning parameter. To the best of our knowledge, no such methods exist elsewhere. The method is illustrated using a pivotal study which introduced IV estimation to epidemiologists. Here, we demonstrate that the conclusion of this paper indeed hinges on these additional distributional assumptions. R-code is provided in the Supporting Information.     

Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices

Principal component analysis is a widely used ''dimension reduction'' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from k(k + 1)/2 to m(2k - m + 1)/2 for k effects and m principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via restricted maximum likelihood using derivatives of the likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.     

ml‐relate: a computer program for maximum likelihood estimation of relatedness and relationship

Genetic data are useful for estimating the genealogical relationship or relatedness between individuals of unknown ancestry. We present a computer program, ml ‐relate that calculates maximum likelihood estimates of relatedness and relationship. ml ‐relate is designed for microsatellite data and can accommodate null alleles. It uses simulation to determine which relationships are consistent with genotype data and to compare putative relationships with alternatives. ml ‐relate runs on the Microsoft Windows operating system and is available from http://www.montana.edu/kalinowski .