scholarly journals Evidence of Absence Treated as Absence of Evidence: The Effects of Variation in the Number and Distribution of Gaps Treated as Missing Data on the Results of Standard Maximum Likelihood Analysis

2019 ◽  
Author(s):  
Denis Jacob Machado ◽  
Santiago Castroviejo-Fisher ◽  
Taran Grant

We evaluated the effects of variation in the number and distribution of gaps (i.e., no base; coded as IUPAC “.” or “–”) treated as missing data (i.e., any base, coded as “?” or IUPAC “N”) in standard maximum likelihood (ML) analysis. We obtained alignments with variable numbers and arrangements of gaps by aligning seven diverse empirical datasets under different gap opening costs using MAFFT. We selected the optimal substitution model for each alignment using the corrected Akaike Information Criterion (AICc) in jModelTest2 and searched for the optimal trees for each alignment using default search parameters and the selected models in GARLI. We also employed a Monte Carlo approach to randomly insert gaps (treated as missing data) into an empirical dataset to understand more precisely the effects of their variable numbers and distributions. To compare alignments quantitatively, we used several measures to quantify the number and distribution of gaps in all alignments (e.g., alignment length, total number of gaps, total number of characters containing gaps, number of gap openings). We then used these variables to derive four indices (ranging from 0 to 1) that summarize the distribution of gaps both within and among terminals, including an index that takes into account their optimization on the tree. Our most important observation is that ML scores correlate negatively with gap opening costs, and the amount of missing data. These variables also cause unpredictable effects on tree topologies. We discuss the implications of our results for the traditional and tree-alignment approaches in ML.

Genetics ◽  
1996 ◽  
Vol 143 (4) ◽  
pp. 1819-1829 ◽  
Author(s):  
G Thaller ◽  
L Dempfle ◽  
I Hoeschele

Abstract Maximum likelihood methodology was applied to determine the mode of inheritance of rare binary traits with data structures typical for swine populations. The genetic models considered included a monogenic, a digenic, a polygenic, and three mixed polygenic and major gene models. The main emphasis was on the detection of major genes acting on a polygenic background. Deterministic algorithms were employed to integrate and maximize likelihoods. A simulation study was conducted to evaluate model selection and parameter estimation. Three designs were simulated that differed in the number of sires/number of dams within sires (10/10, 30/30, 100/30). Major gene effects of at least one SD of the liability were detected with satisfactory power under the mixed model of inheritance, except for the smallest design. Parameter estimates were empirically unbiased with acceptable standard errors, except for the smallest design, and allowed to distinguish clearly between the genetic models. Distributions of the likelihood ratio statistic were evaluated empirically, because asymptotic theory did not hold. For each simulation model, the Average Information Criterion was computed for all models of analysis. The model with the smallest value was chosen as the best model and was equal to the true model in almost every case studied.


2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Helena Mouriño ◽  
Maria Isabel Barão

Missing-data problems are extremely common in practice. To achieve reliable inferential results, we need to take into account this feature of the data. Suppose that the univariate data set under analysis has missing observations. This paper examines the impact of selecting an auxiliary complete data set—whose underlying stochastic process is to some extent interdependent with the former—to improve the efficiency of the estimators for the relevant parameters of the model. The Vector AutoRegressive (VAR) Model has revealed to be an extremely useful tool in capturing the dynamics of bivariate time series. We propose maximum likelihood estimators for the parameters of the VAR(1) Model based on monotone missing data pattern. Estimators’ precision is also derived. Afterwards, we compare the bivariate modelling scheme with its univariate counterpart. More precisely, the univariate data set with missing observations will be modelled by an AutoRegressive Moving Average (ARMA(2,1)) Model. We will also analyse the behaviour of the AutoRegressive Model of order one, AR(1), due to its practical importance. We focus on the mean value of the main stochastic process. By simulation studies, we conclude that the estimator based on the VAR(1) Model is preferable to those derived from the univariate context.


Genetics ◽  
1972 ◽  
Vol 72 (4) ◽  
pp. 709-719
Author(s):  
Peter E Smouse ◽  
Ken-Ichi Kojima

ABSTRACT Statistical techniques are presented for the analysis of geographic variation in allelic frequencies. Likelihood ratio test criteria are derived from a multinominal sampling distribution, and are used to answer three questions. (1) Are there geographic differences in allelic frequencies? (2) Are population differences in allelic frequencies associated with environmental differences? (3) Is there any residual "lack of fit" variation among populations, after accounting for that variation associated with environmental differences? The two- and three-allele cases are explicitly treated, and the extension to more alleles is indicated.


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