Bias‐Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter

Saha, Krishna K.; Paul, S. R.

doi:10.1111/j.0006-341x.2005.030833.x

Cited by 99 publications

(64 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Note that the parameter ϕ i is used to measure the extra variability compared to the Poisson distribution, and is usually called the extra-dispersion parameter. Several parametric forms for the NB distributions exist, and we use the form found in Saha and Paul [28].…”

Section: Based On Nb Modelmentioning

confidence: 99%

“…The ML estimate ˆi φ of ϕ i can be obtained by maximizing the log-likelihood of the NB model, or solving the estimating equations discussed by Saha and Paul [28].…”

Section: Based On Nb Modelmentioning

confidence: 99%

“…For each given combination, we compute the corresponding coverage probability by the proportion of intervals that included the true value of the parameter of interest, MR. Note those confidence intervals (CI) based on ML estimates of the extra-dispersion parameters did not exist for some samples [28], and these were discarded. Further note that a confidence interval is good if it is able to guarantee its CPs close to the nominal coverage level.…”

Section: Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Saha¹

2013

J Biomet Biostat

View full text Add to dashboard Cite

Responses in the form of counts arise in many clinical trials and epidemiological studies, and are usually extradispersed. When one wishes to estimate the treatment effect in comparison with a placebo in clinical trials, confidence intervals are frequently used. It is of common interest in many clinical trials and epidemiological studies, to obtain the confidence interval for one of the two quantities, mean difference and mean ratio. The preference of one measure over the other depends on the design of the study. In many situations, the mean ratio is more relevant than the difference of means. Confidence interval procedures for the mean difference between treatment and control groups in the analysis of such extra-dispersed counts have been studied recently, but no attention has been paid to investigating the problem of confidence interval construction for the mean ratio. In this article, we develop several asymptotic confidence interval procedures for the mean ratio, by using the delta method, to extend the variance of a single mean estimate to the variance of the mean ratio estimate. The simulation studies indicate that all procedures perform reasonably well in terms of coverage. However, the interval based on the generalized estimating equation approach, using the logarithmic transformation, performs uniformly best in terms of coverage, expected width and location, and is preferable to the other intervals, in most of the situations considered here. Finally, three real-life examples from clinical trials are analyzed to illustrate the proposed confidence interval procedures.

show abstract

Section: Based On Nb Modelmentioning

confidence: 99%

“…The ML estimate ˆi φ of ϕ i can be obtained by maximizing the log-likelihood of the NB model, or solving the estimating equations discussed by Saha and Paul [28].…”

Section: Based On Nb Modelmentioning

confidence: 99%

Section: Simulationsmentioning

confidence: 99%

See 1 more Smart Citation

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Saha¹

2013

J Biomet Biostat

View full text Add to dashboard Cite

show abstract

“…Because of their widespread use, it is important to have simple, efficient and accurate estimators for multinomial and negative multinomial distributions. The estimators known to us are based on complicated concepts: bias corrected maximum likelihood estimator for negative binomial dispersion parameter (Saha and Paul (2005)); bootstrap confidence intervals for the difference of two independent binomial proportions (Lin et al (2009)); bias reducing penalized maximum likelihood estimators for parameters of a multinomial logistic regression (Kosmidis and Firth (2011)); jackknife estimators for binomial and multinomial parameters (Withers and Nadarajah (2013)); and others.…”

Section: Introductionmentioning

confidence: 99%

Estimators for a Class of Power Series Families

Withers¹,

Nadarajah

2015

JJSS

View full text Add to dashboard Cite

show abstract

“…When k is an integer, the NBD becomes the Pascal distribution, and the geometric distribution corresponds to k=1. The log series distribution occurs when zeros are missing and as k→∞ (Saha and Paul, 2005).…”

Section: Introductionmentioning

confidence: 99%

Evaluation of Statistical Models for Analysis of Insect, Disease and Weed Abundance and Incidence Data

Sileshi¹

2007

East African Journal of Sciences

View full text Add to dashboard Cite

Analysis of variance (ANOVA) has been a fundamental method used for analysis of abundance and incidence data. However, abundance and incidence data often violate the assumptions of ANOVA. Researchers often ignore ANOVA assumptions, transform the data using arbitrarily chosen functions and then fail to evaluate whether or not the transformation actually corrected the problem. The statistical power of the tests used is also seldom reported. Therefore, the objectives of this paper are to demonstrate (1) implications of using arbitrarily chosen transformations and ANOVA to the validity of statistical inference on pest abundance and incidence and (2) the application of LMMs and GLMs for efficient analysis of such data. Abundance data were analyzed assuming normal, Poisson and negative binomial error distributions. Incidence data were analyzed assuming normal and binomial error distributions. Among the data transformation functions, logarithmic transformation gave better description of abundance data compared with square root. Working logits were better than angular or square root transformation of incidence data. The study has also demonstrated that the choice of transformation can influence the statistical significance and power of test. Transformation of either abundance or incidence data did not necessarily ensure normality or variance homogeneity. According to the Akaike information criterion (AIC), a GLM assuming negative binomial error distribution was better for description of most abundance datasets compared with a GLM assuming Poisson error distribution or LMM. LMM based on working logits also gave a better description of the data than a GLM assuming binomial distribution. It is concluded that LMMs and GLMs simultaneously consider the effect of treatments and heterogeneity of variance and hence are more appropriate for analysis of abundance and incidence data than ordinary ANOVA.

show abstract

Bias‐Corrected Maximum Likelihood Estimator of the Negative Binomial Dispersion Parameter

Cited by 99 publications

References 26 publications

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Estimating the Treatment Effect in the Analysis of Extra-Dispersed Count Response Data from Clinical Trials

Estimators for a Class of Power Series Families

Evaluation of Statistical Models for Analysis of Insect, Disease and Weed Abundance and Incidence Data

Contact Info

Product

Resources

About