182 research outputs found
Model Criticism for Growth Curve Models via Posterior Predictive Model Checking
No full textabstract: Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values.
In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research.Dissertation/ThesisDoctoral Dissertation Educational Psychology 201
Woman’s Magic as a Power of Resistance and Subversion: Morgan le Fay in Thomas Malory’s Morte d’Arthur
No full textDiscovery and Communication of Important Marketing Findings: Evidence and Proposals
No full textMy review of empirical research on scientific publication led to the following conclusions. Three criteria are useful for identifying whether findings are important: replication, validity, and usefulness. A fourth criterion, surprise, applies in some situations. Based on these criteria, important findings resulting from academic research in marketing seem to be rare. To a large extent, this rarity is due to a reward system that is built around subjective peer review. Rather than using peer review as a secret screening process, using an open process likely will improve papers and inform readers. Researchers, journals, business schools, funding agencies, and professional organizations can all contribute to improving the process. For example, researchers should do directed research on papers that contribute to principles. Journals should invite papers that contribute to principles. Business school administrators should reward researchers who make important findings. Funding agencies should base decisions on researchers' prior success in making important findings, and professional organizations should maintain web sites that describe what is known about principles and what research is needed on principles.marketing, marketing findings
The Analysis of Very Small Samples of Repeated Measurements
No full textThe statistical analysis of repeated measures or longitudinal data always requires the
accommodation of the covariance structure of the repeated measurements at some
stage in the analysis. The general linear mixed model is often used for such analyses,
and allows for the specification of both a mean model and a covariance structure.
Often the covariance structure itself is not of direct interest, but only a means to
producing valid inferences about the response. This thesis considers methods for
the analysis of repeated measurements which arise from very small samples.
In Part 1, existing methods of analysis are shown to be inadequate for very small
samples. More precisely, statistical measures of goodness of fit are not necessarily
the right measure of the appropriateness of a covariance structure and inferences
based on conventional Wald type procedures (with small sample adjustments) do
not approximate sufficiently well their nominal properties when data are unbalanced
or incomplete.
In Part 2, adaptive-estimation techniques are considered for the sample covariance
matrix which smooth between unstructured and structured forms; 'direct' smoothing, a weighted average of the unstructured and structured estimates, and an estimate chosen via penalised likelihood. Whilst attractive in principle, these approaches are shown to have little success in practice, being critically dependent on
the 'correct' choice of smoothing structure.
Part 3 considers methods which are less dependent on the covariance structure. A
generalisation of a small sample adjustment to the empirical sandwich estimator
is developed which accounts for its inherent bias and increased variance. This has
nominal properties but lacks power. Also, a modification to Box's correction, an
ANOVA F-statistic which accounts for departures from independence, is given which
has both nominal properties and acceptable power.
Finally, Part 4 recommends the adoption of the modified Box statistic for repeated
measurements data where the sample size is very small
Assessing the freshwater distribution of yellow eel
No full textIn the global context of the decline in wild species, modeling the distribution of populations is a crucial aspect of ecological management. This can be a major challenge, especially for species, such as the European eel, that have complex life cycles, exhibit cryptic behavior, or migrate over long distances. A review of the literature suggests that eel size data could be used to assess and analyze freshwater distribution of eel. We argue that analyses based on small yellow eels (≤ 300 mm) along the longitudinal course of rivers could provide a valuable tool for population monitoring. We propose a standardized catchment recruitment index and a colonization index based on the probability of occurrence (presence/absence data) using logistic models for different size classes. The model developed here provides a convenient guide for assessing yellow eel stages in freshwater areas, and should have concrete applications for management of the species
The analysis of very small samples of repeated measurements I: an adjusted sandwich estimator
No full textThe statistical analysis of repeated measures or longitudinal data always requires the accommodation of the
covariance structure of the repeated measurements at some stage in the analysis. The general linear mixed
model is often used for such analyses, and allows for the specification of both a mean model and a covariance
structure. Often the covariance structure itself is not of direct interest, but only a means to producing valid inferences about the response. Existing methods of analysis are often inadequate where the sample size is small. More precisely, statistical measures of goodness of fit are not necessarily the right measure of the appropriateness of a covariance structure and inferences based on conventional Wald type procedures do not approximate sufficiently well
their nominal properties when data are unbalanced or incomplete. This is shown to be the case when adopting
the Kenward-Roger adjustment where the sample size is very small. A generalization of an approach to Wald tests using a bias adjusted empirical sandwich estimator for the covariance matrix of the fixed effects from generalized estimating equations is developed for Gaussian repeated measurements. This is shown to attain the correct test size but has very low power
Nonparametric tests for informative selection and small area estimation for reconciling survey estimates
No full textIncludes bibliographical references.2020 Summer.Two topics in the analysis of complex survey data are addressed: testing for informative selection and addressing temporal discontinuities due to survey redesign. Informative selection, in which the distribution of response variables given that they are sampled is different from their distribution in the population, is pervasive in modern complex surveys. Failing to take such informativeness into account could produce severe inferential errors, such as biased parameter estimators, wrong coverage rates of confidence intervals, incorrect test statistics, and erroneous conclusions. While several parametric procedures exist to test for informative selection in the survey design, it is often hard to check the parametric assumptions on which those procedures are based. We propose two classes of nonparametric tests for informative selection, each motivated by a nonparametric test for two independent samples. The first nonparametric class generalizes classic two-sample tests that compare empirical cumulative distribution functions, including Kolmogorov–Smirnov and Cramér–von Mises, by comparing weighted and unweighted empirical cumulative distribution functions. The second nonparametric class adapts two-sample tests that compare distributions based on the maximum mean discrepancy to the setting of weighted and unweighted distributions. The asymptotic distributions of both test statistics are established under the null hypothesis of noninformative selection. Simulation results demonstrate the usefulness of the asymptotic approximations, and show that our tests have competitive power with parametric tests in a correctly specified parametric setting while achieving greater power in misspecified scenarios. Many surveys face the problem of comparing estimates obtained with different methodology, including differences in frames, measurement instruments, and modes of delivery. Differences may exist within the same survey; for example, multi-mode surveys are increasingly common. Further, it is inevitable that surveys need to be redesigned from time to time. Major redesign of survey processes could affect survey estimates systematically, and it is important to quantify and adjust for such discontinuities between the designs to ensure comparability of estimates over time. We propose a small area estimation approach to reconcile two sets of survey estimates, and apply it to two surveys in the Marine Recreational Information Program (MRIP). We develop a log-normal model for the estimates from the two surveys, accounting for temporal dynamics through regression on population size and state-by-wave seasonal factors, and accounting in part for changing coverage properties through regression on wireless telephone penetration. Using the estimated design variances, we develop a regression model that is analytically consistent with the log-normal mean model. We use the modeled design variances in a Fay-Herriot small area estimation procedure to obtain empirical best linear unbiased predictors of the reconciled effort estimates for all states and waves, and provide an asymptotically valid mean square error approximation
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