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Standardized Regression Coefficients and Newly Proposed Estimators for [Formula: see text] in Multiply Imputed Data.

ABSTRACT: Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing [Formula: see text] for significance have long been established. However, there is still no general agreement on how to combine the point estimators of [Formula: see text] in multiple regression applied to multiply imputed datasets. Additionally, no combination rules for standardized regression coefficients and their confidence intervals seem to have been developed at all. In the current article, two sets of combination rules for the standardized regression coefficients and their confidence intervals are proposed, and their statistical properties are discussed. Additionally, two improved point estimators of [Formula: see text] in multiply imputed data are proposed, which in their computation use the pooled standardized regression coefficients. Simulations show that the proposed pooled standardized coefficients produce only small bias and that their 95% confidence intervals produce coverage close to the theoretical 95%. Furthermore, the simulations show that the newly proposed pooled estimates for [Formula: see text] are less biased than two earlier proposed pooled estimates.

SUBMITTER: van Ginkel JR

PROVIDER: S-EPMC7186259 | biostudies-literature | 2020 Mar

REPOSITORIES: biostudies-literature

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Standardized Regression Coefficients and Newly Proposed Estimators for [Formula: see text] in Multiply Imputed Data.

van Ginkel Joost R JR

Psychometrika 20200311 1

Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing [Formula: see text] for significance have long been established. However, there is still no general agreement on how to combine the point est ...[more]

PMID: 32162232

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Project description:The experimental value for the isospin amplitude [Formula: see text] in [Formula: see text] decays has been successfully explained within the standard model (SM), both within the large [Formula: see text] approach to QCD and by QCD lattice calculations. On the other hand within the large [Formula: see text] approach the value of [Formula: see text] is by at least [Formula: see text] below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in [Formula: see text] comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless [Formula: see text] gauge boson with a flavour-violating left-handed coupling [Formula: see text] and an approximately universal flavour diagonal right-handed coupling [Formula: see text] to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to [Formula: see text]. This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator [Formula: see text] to [Formula: see text]. A large fraction of the missing piece in the [Formula: see text] rule can be explained in this manner for [Formula: see text] in the reach of the LHC, while satisfying the constraints from [Formula: see text], [Formula: see text], [Formula: see text], LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling [Formula: see text] and of enhanced matrix elements of [Formula: see text] left-right operators allows one to satisfy simultaneously the constraints from [Formula: see text] and [Formula: see text], although this requires some fine-tuning. We identify the quartic correlation between [Formula: see text] contributions to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The tests of this proposal will require much improved evaluations of [Formula: see text] and [Formula: see text] within the SM, of [Formula: see text] as well as precise tree-level determinations of [Formula: see text] and [Formula: see text]. We present correlations between [Formula: see text], [Formula: see text] and [Formula: see text] with and without the [Formula: see text] rule constraint and generalise the whole analysis to [Formula: see text] with colour ([Formula: see text]) and [Formula: see text] with FCNC couplings. In the latter case no improvement on [Formula: see text] can be achieved without destroying the agreement of the SM with the data on [Formula: see text]. Moreover, this scenario is very tightly constrained by [Formula: see text]. On the other hand, in the context of the [Formula: see text] rule [Formula: see text] is even more effective than [Formula: see text]: it provides the missing piece in [Formula: see text] for [Formula: see text]-[Formula: see text].

Project description:The Josephson effect in point contacts between an "ordinary" superconductor [Formula: see text]In[Formula: see text] ([Formula: see text]) and single crystals of the Fe-based superconductor Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text] ([Formula: see text]), was investigated. In order to shed light on the order parameter symmetry of Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text], the dependence of the Josephson supercurrent [Formula: see text] on the temperature and on [Formula: see text] with [Formula: see text] was studied. The dependencies of the critical current on temperature [Formula: see text] and of the amplitudes of the first current steps of the current-voltage characteristic [Formula: see text] [Formula: see text] on the power of microwave radiation with frequency [Formula: see text] were measured. It is shown that the dependencies [Formula: see text] are close to the well-known Ambegaokar-Baratoff (AB) dependence for tunnel contacts between "ordinary" superconductors and to the dependence calculated by Burmistrova et al. (Phys Rev B 91, 214501 (2015)) for microshorts between an "ordinary" superconductor and a two-band superconductor with [Formula: see text] order parameter symmetry at certain values of the transparency of boundaries and thickness of the transition layer. It is found that the dependencies [Formula: see text] cannot be approximated within the resistively shunted model using the normalized microwave frequencies [Formula: see text] with characteristic voltages [Formula: see text], [Formula: see text]-normal resistance of the contact) found from the low-voltage parts of the current-voltage characteristics. The reasons for this failure are discussed and a method is proposed for accurately determining the value of [Formula: see text], which takes into account all the features of the point contact affecting the period of the dependence [Formula: see text]. An analysis of the [Formula: see text] and [Formula: see text] dependencies shows that the superconducting current of the Josephson contacts under investigation is proportional to the [Formula: see text] of the phase difference [Formula: see text], [Formula: see text]. The implications of these results on the symmetry of the order parameter are also discussed.

Dataset Information

Standardized Regression Coefficients and Newly Proposed Estimators for [Formula: see text] in Multiply Imputed Data.

Publications

Standardized Regression Coefficients and Newly Proposed Estimators for [Formula: see text] in Multiply Imputed Data.

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