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"Proportions"
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Control Function Methods in Applied Econometrics
This paper provides an overview of control function (CF) methods for solving the problem of endogenous explanatory variables (EEVs) in linear and nonlinear models. CF methods often can be justified in situations where \"plug-in\" approaches are known to produce inconsistent estimators of parameters and partial effects. Usually, CF approaches require fewer assumptions than maximum likelihood, and CF methods are computationally simpler. The recent focus on estimating average partial effects, along with theoretical results on nonparametric identification, suggests some simple, flexible parametric CF strategies. The CF approach for handling discrete EEVs in nonlinear models is more controversial but approximate solutions are available.
Journal Article
The McNemar test for binary matched-pairs data: mid-p and asymptotic are better than exact conditional
Background
Statistical methods that use the mid-
p
approach are useful tools to analyze categorical data, particularly for small and moderate sample sizes. Mid-
p
tests strike a balance between overly conservative exact methods and asymptotic methods that frequently violate the nominal level. Here, we examine a mid-
p
version of the McNemar exact conditional test for the analysis of paired binomial proportions.
Methods
We compare the type I error rates and power of the mid-
p
test with those of the asymptotic McNemar test (with and without continuity correction), the McNemar exact conditional test, and an exact unconditional test using complete enumeration. We show how the mid-
p
test can be calculated using eight standard software packages, including Excel.
Results
The mid-
p
test performs well compared with the asymptotic, asymptotic with continuity correction, and exact conditional tests, and almost as good as the vastly more complex exact unconditional test. Even though the mid-
p
test does not guarantee preservation of the significance level, it did not violate the nominal level in any of the 9595 scenarios considered in this article. It was almost as powerful as the asymptotic test. The exact conditional test and the asymptotic test with continuity correction did not perform well for any of the considered scenarios.
Conclusions
The easy-to-calculate mid-
p
test is an excellent alternative to the complex exact unconditional test. Both can be recommended for use in any situation. We also recommend the asymptotic test if small but frequent violations of the nominal level is acceptable.
Journal Article
Vertical and Horizontal Proportions of the Face and their Correlation to Phi in a South Indian Population
Background:
With the shift in focus from the hard to soft tissue in orthodontic diagnosis and treatment planning, the scope of orthodontic treatment has grown beyond achieving an ideal occlusion, also to achieve ideal aesthetic facial proportions. Since time immemorial, the various horizontal and vertical proportions of an ideal face is considered to follow the golden/divine ratio.
Aim:
The aim of this study is to assess the vertical and horizontal proportions of the face and their relation of phi in males and females of Dakshina Kannada population.
Materials and Methods:
The study was carried out on 100 subjects, which included 50 males and 50 females, aged between 18 and 30 years. Photographs were taken under standardized condition and adjusted to a standardized image size (5″ × 4″). Adobe Photoshop CS5.1 software was used for making all the measurements. A total of 11 vertical and horizontal ratios were independently measured for males and females, and their relation to phi was assessed. The data were subjected to Shapiro-Wilk test for testing the normality. Homogeneity of variance assumption was tested by using Levene statistic homogeneity of variance. One sample t test was used for the comparison between phi and mean vertical and horizontal ratios in males and females.
Results:
In males and females of the Dakshina Kannada, a statistically significant correlation was seen between all the horizontal and vertical facial proportions and phi (p < 0.05). Between male and female groups, a significant difference was noted in the intertemporal/intercanthal ratio, interalae/nose width and Intereye-soft menton/ala-soft menton (p < 0.05).
Conclusion:
Golden proportion can be used as a guideline in orthodontic treatment planning. However, it should not be the decisive factor in determining the facial attractiveness.
Journal Article
Architecture and Narrative
Architecture is often seen as the art of a thinking mind that arranges, organizes and establishes relationships between the parts and the whole. It is also seen as the art of designing spaces, which we experience through movement and use. Conceptual ordering, spatial and social narrative are fundamental to the ways in which buildings are shaped, used and perceived. Examining and exploring the ways in which these three dimensions interact in the design and life of buildings, this intriguing book will be of use to anyone with an interest in the theory of architecture and architecture's relationship to the cultural human environment.
eBook
Discourse-Linked DPs as Covert Partitives
The paper studies the conditions that determine the Discourse-Linked or non-Discourse-Linked status of noun-less Determiner Phrases introduced by different determiners, in Italian and in English. For instance, given the sentence Ten bombs exploded yesterday, the continuation [Three] were cluster bombs tends to have a meaning equivalent to 'three of the bombs that exploded’ (D-Linked), while [Three] will explode today is understood as 'three (different) bombs’ (non D-Linked). Beside world-knowledge, the syntax of the determiners and their position with respect to the verb affect the availability of DL/non-DL readings. This and other facts undermine an analysis cast purely in terms of semantic domain restrictions, and suggest that DL readings are due to the presence of a covert partitive structure. While perhaps intuitive, this idea faces various issues in Italian, due to its interactions with the syntax of the pro-form ne. We show that an NP-based structure for numeral and proportion-based partitives (three/half of the bombs) is actually compatible with the facts, and offers a cue on the nature of sub-DP pro-forms and their uses.
Journal Article
Maxillary Anterior Teeth Dimensions and Relative Width Proportions: A Narrative Literature Review
Predictable results in the aesthetic treatment of anterior teeth can be obtained by resorting to the concept of dental aesthetics and, in particular, defining the ideal tooth dimensions and proportions to obtain a harmonious smile. Considering the great variety of articles dealing with the topic, and the lack of updated reviews, this narrative literature review aims to evaluate current knowledge on anterior teeth dimensions and to verify the existence and the potential applications of the anterior teeth proportioning theories (Golden Proportion, Golden Percentage, RED Proportion, and Golden Rectangle). PubMed, Embase, Cochrane Library, and Google Scholar databases were comprehensively searched using different keywords and term combinations. The research includes articles published up to June 2023, no time limits were set, and only articles in English were included. Inclusion criteria comprehended reviews, clinical studies, and in-vitro studies. A total of 66 articles were selected. Two main topics were identified: “Anterior teeth dimensions”, “Golden Proportions, Golden Percentage, RED Proportions, and Golden Rectangle”. As far as tooth dimensions are concerned, different width ranges are recognized for men and women and for different ethnic groups. Perfectly symmetric contralateral elements are found in low percentages of subjects. The correlation between dental dimensions and facial parameters is not always present, and it strongly depends on the sample’s ethnicity and gender. Ideal tooth proportions were only partially identified.
Journal Article
Optimal Subsampling for Large Sample Logistic Regression
For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least-square estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this article, we propose fast subsampling algorithms to efficiently approximate the maximum likelihood estimate in logistic regression. We first establish consistency and asymptotic normality of the estimator from a general subsampling algorithm, and then derive optimal subsampling probabilities that minimize the asymptotic mean squared error of the resultant estimator. An alternative minimization criterion is also proposed to further reduce the computational cost. The optimal subsampling probabilities depend on the full data estimate, so we develop a two-step algorithm to approximate the optimal subsampling procedure. This algorithm is computationally efficient and has a significant reduction in computing time compared to the full data approach. Consistency and asymptotic normality of the estimator from a two-step algorithm are also established. Synthetic and real datasets are used to evaluate the practical performance of the proposed method. Supplementary materials for this article are available online.
Journal Article
Bayesian Inference for Logistic Models Using Pólya–Gamma Latent Variables
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Pólya–Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negative binomial regression, nonlinear mixed-effect models, and spatial models for count data. In each case, our data-augmentation strategy leads to simple, effective methods for posterior inference that (1) circumvent the need for analytic approximations, numerical integration, or Metropolis–Hastings; and (2) outperform other known data-augmentation strategies, both in ease of use and in computational efficiency. All methods, including an efficient sampler for the Pólya–Gamma distribution, are implemented in the R package BayesLogit . Supplementary materials for this article are available online.
Journal Article
WHICH BRIDGE ESTIMATOR IS THE BEST FOR VARIABLE SELECTION?
We study the problem of variable selection for linear models under the high-dimensional asymptotic setting, where the number of observations n grows at the same rate as the number of predictors p. We consider two-stage variable selection techniques (TVS) in which the first stage uses bridge estimators to obtain an estimate of the regression coefficients, and the second stage simply thresholds this estimate to select the “important” predictors. The asymptotic false discovery proportion (AFDP) and true positive proportion (ATPP) of these TVS are evaluated. We prove that for a fixed ATPP, in order to obtain a smaller AFDP, one should pick a bridge estimator with smaller asymptotic mean square error in the first stage of TVS. Based on such principled discovery, we present a sharp comparison of different TVS, via an in-depth investigation of the estimation properties of bridge estimators. Rather than “orderwise” error bounds with loose constants, our analysis focuses on precise error characterization. Various interesting signal-to-noise ratio and sparsity settings are studied. Our results offer new and thorough insights into high-dimensional variable selection. For instance, we prove that a TVS with Ridge in its first stage outperforms TVS with other bridge estimators in large noise settings; two-stage LASSO becomes inferior when the signal is rare and weak. As a by-product, we show that two-stage methods outperform some standard variable selection techniques, such as LASSO and Sure Independence Screening, under certain conditions.
Journal Article