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1.
A scaled difference test statistic
[(T)\tilde]d\tilde{T}{}_{d}
that can be computed from standard software of structural equation models (SEM) by hand calculations was proposed in Satorra
and Bentler (Psychometrika 66:507–514, 2001). The statistic
[(T)\tilde]d\tilde{T}_{d}
is asymptotically equivalent to the scaled difference test statistic
[`(T)]d\bar{T}_{d}
introduced in Satorra (Innovations in Multivariate Statistical Analysis: A Festschrift for Heinz Neudecker, pp. 233–247, 2000), which requires more involved computations beyond standard output of SEM software. The test statistic
[(T)\tilde]d\tilde{T}_{d}
has been widely used in practice, but in some applications it is negative due to negativity of its associated scaling correction.
Using the implicit function theorem, this note develops an improved scaling correction leading to a new scaled difference
statistic
[`(T)]d\bar{T}_{d}
that avoids negative chi-square values. 相似文献
2.
3.
4.
MLJ van de Vel 《Studia Logica》2010,95(3):379-405
A first-order theory T{{\mathcal T}} has the Independence Property provided
T \vdash (Q)(FT F1 ú. . .úFn){{{\mathcal T} \, \, \vdash (Q)(\Phi \Rightarrow {\Phi_1} \vee.\,.\,.\vee {\Phi_n})}} implies
T \vdash (Q)(FT Fi){{{\mathcal T} \, \, \vdash (Q)(\Phi \Rightarrow {\Phi_i})}} for some i whenever F,F1, . . . ,Fn{{\Phi,\Phi_1,\,.\,.\,.\,,\Phi_n}} are formulae of a suitable type and (Q) is any quantifier sequence. Variants of this property have been noticed for some time in logic programming and in linear
programming. 相似文献
5.
After defining, for each many-sorted signature Σ = (S, Σ), the category Ter(Σ), of generalized terms for Σ (which is the dual of the Kleisli category for
\mathbb TS{\mathbb {T}_{\bf \Sigma}}, the monad in Set
S
determined by the adjunction
TS \dashv GS{{\bf T}_{\bf \Sigma} \dashv {\rm G}_{\bf \Sigma}} from Set
S
to Alg(Σ), the category of Σ-algebras), we assign, to a signature morphism d from Σ to Λ, the functor dà{{\bf d}_\diamond} from Ter(Σ) to Ter(Λ). Once defined the mappings that assign, respectively, to a many-sorted signature the corresponding category of generalized
terms and to a signature morphism the functor between the associated categories of generalized terms, we state that both mappings
are actually the components of a pseudo-functor Ter from Sig to the 2-category Cat. Next we prove that there is a functor TrΣ, of realization of generalized terms as term operations, from Alg(Σ) × Ter(Σ) to Set, that simultaneously formalizes the procedure of realization of generalized terms and its naturalness (by taking into account
the variation of the algebras through the homomorphisms between them). We remark that from this fact we will get the invariance
of the relation of satisfaction under signature change. Moreover, we prove that, for each signature morphism d from Σ to Λ, there exists a natural isomorphism θ
d from the functor TrL °(Id ×dà){{{\rm Tr}^{\bf {\bf \Lambda}} \circ ({\rm Id} \times {\bf d}_\diamond)}} to the functor TrS °(d* ×Id){{\rm Tr}^{\bf \Sigma} \circ ({\bf d}^* \times {\rm Id})}, both from the category Alg(Λ) × Ter(Σ) to the category Set, where d* is the value at d of the arrow mapping of a contravariant functor Alg from Sig to Cat, that shows the invariant character of the procedure of realization of generalized terms under signature change. Finally,
we construct the many-sorted term institution by combining adequately the above components (and, in a derived way, the many-sorted
specification institution), but for a strict generalization of the standard notion of institution. 相似文献
6.
7.
Philip Kremer 《Studia Logica》2016,104(3):487-502
The simplest combination of unimodal logics \({\mathrm{L}_1 \rm and \mathrm{L}_2}\) into a bimodal logic is their fusion, \({\mathrm{L}_1 \otimes \mathrm{L}_2}\), axiomatized by the theorems of \({\mathrm{L}_1 \rm for \square_1 \rm and of \mathrm{L}_2 \rm for \square_{2}}\). Shehtman introduced combinations that are not only bimodal, but two-dimensional: he defined 2-d Cartesian products of 1-d Kripke frames, using these Cartesian products to define the frame product\({\mathrm{L}_1 \times \mathrm{L}_2 \rm of \mathrm{L}_1 \rm and \mathrm{L}_2}\). Van Benthem, Bezhanishvili, ten Cate and Sarenac generalized Shehtman’s idea and introduced the topological product\({\mathrm{L}_1 \times_{t}\mathrm{L}_2}\), using Cartesian products of topological spaces rather than of Kripke frames. Frame products have been extensively studied, but much less is known about topological products. The goal of the current paper is to give necessary and sufficient conditions for the topological product to match the frame product, for Kripke complete extensions of \({\mathrm{S}4: \mathrm{L}_1 \times_t \mathrm{L}_2 = \mathrm{L}_1 \times \mathrm{L}_2 \rm iff \mathrm{L}_1 \supsetneq \mathrm{S}5 \rm or \mathrm{L}_2 \supsetneq \mathrm{S}5 \rm or \mathrm{L}_1, \mathrm{L}_2 = \mathrm{S}5}\). 相似文献
8.
Jeremy Meyers 《Journal of Philosophical Logic》2014,43(1):71-108
Hybrid languages are introduced in order to evaluate the strength of “minimal” mereologies with relatively strong frame definability properties. Appealing to a robust form of nominalism, I claim that one investigated language $\mathcal {H}_{\textsf {m}}$ is maximally acceptable for nominalistic mereology. In an extension $\mathcal {H}_{\textsf {gem}}$ of $\mathcal {H}_{\textsf {m}}$ , a modal analog for the classical systems of Leonard and Goodman (J Symb Log 5:45–55, 1940) and Le?niewski (1916) is introduced and shown to be complete with respect to 0-deleted Boolean algebras. We characterize the formulas of first-order logic invariant for $\mathcal {H}_{\textsf {gem}}$ -bisimulations. 相似文献
9.
Riccardo Bruni 《Studia Logica》2013,101(5):915-932
The paper introduces Hilbert– and Gentzen-style calculi which correspond to systems ${\mathsf{C}_{n}}$ from Gupta and Belnap [3]. Systems ${\mathsf{C}_{n}}$ were shown to be sound and complete with respect to the semantics of finite revision. Here, it is shown that Gentzen-style systems ${\mathsf{GC}_{n}}$ admit a syntactic proof of cut elimination. As a consequence, it follows that they are consistent. 相似文献
10.
Heinrich Wansing 《Journal of Philosophical Logic》2010,39(4):369-393
The trilattice SIXTEEN3\textit{SIXTEEN}_3 is a natural generalization of the well-known bilattice FOUR2\textit{FOUR}_2. Cut-free, sound and complete sequent calculi for truth entailment and falsity entailment in SIXTEEN3\textit{SIXTEEN}_3 are presented. 相似文献
11.
We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such
quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
Presented by Heinrich Wansing 相似文献
12.
Niels G. Waller 《Psychometrika》2011,76(4):634-649
In linear multiple regression, “enhancement” is said to occur when R
2=b′r>r′r, where b is a p×1 vector of standardized regression coefficients and r is a p×1 vector of correlations between a criterion y and a set of standardized regressors, x. When p=1 then b≡r and enhancement cannot occur. When p=2, for all full-rank R
xx≠I, R
xx=E[xx′]=V
Λ
V′ (where V
Λ
V′ denotes the eigen decomposition of R
xx; λ
1>λ
2), the set B1:={bi:R2=bi¢ri=ri¢ri;0 < R2 £ 1}\boldsymbol{B}_{1}:=\{\boldsymbol{b}_{i}:R^{2}=\boldsymbol{b}_{i}'\boldsymbol{r}_{i}=\boldsymbol{r}_{i}'\boldsymbol{r}_{i};0R2 £ 1;R2lp £ ri¢ri < R2}0p≥3 (and λ
1>λ
2>⋯>λ
p
), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B
1 occurs at the intersection of two hyper-ellipsoids in ℝ
p
. Equations are provided for populating the sets B
1 and B
2 and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with λ
p
(the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying
geometry of enhancement in population, multiple-regression models. R code for simulating population regression models that exhibit enhancement of any degree and any number of predictors is included
in Appendices A and B. 相似文献
13.
Ja?kowski’s discussive logic D2 was formulated with the help of the modal logic S5 as follows (see [7, 8]): \({A \in {D_{2}}}\) iff \({\ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\rm S}5}\), where (–)? is a translation of discussive formulae from Ford into the modal language. We say that a modal logic L defines D2 iff \({{\rm D}_{2} = \{A \in {\rm For^{\rm d}} : \ulcorner\diamond{{A}^{\bullet}}\urcorner \in {\it L}\}}\). In [14] and [10] were respectively presented the weakest normal and the weakest regular logic which (?): have the same theses beginning with ‘\({\diamond}\)’ as S5. Of course, all logics fulfilling the above condition, define D2. In [10] it was prowed that in the cases of logics closed under congruence the following holds: defining D2 is equivalent to having the property (?). In this paper we show that this equivalence holds also for all modal logics which are closed under replacement of tautological equivalents (rte-logics).We give a general method which, for any class of modal logics determined by a set of joint axioms and rules, generates in the given class the weakest logic having the property (?). Thus, for the class of all modal logics we obtain the weakest modal logic which owns this property. On the other hand, applying the method to various classes of modal logics: rte-logics, congruential, monotonic, regular and normal, we obtain the weakest in a given class logic defining D2. 相似文献
14.
We present some equivalent conditions for a quasivariety of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if are nontrivial, then there exists such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5].
Presented by Jacek Malinowski 相似文献
15.
In his milestone textbook Lattice Theory, Garrett Birkhoff challenged his readers to develop a ??common abstraction?? that includes Boolean algebras and latticeordered groups as special cases. In this paper, after reviewing the past attempts to solve the problem, we provide our own answer by selecting as common generalization of ${\mathcal{B} \mathcal{A}}$ and ${\mathcal{L} \mathcal{G}}$ their join ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ in the lattice of subvarieties of ${\mathcal{F} \mathcal{L}}$ (the variety of FL-algebras); we argue that such a solution is optimal under several respects and we give an explicit equational basis for ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ relative to ${\mathcal{F} \mathcal{L}}$ . Finally, we prove a Holland-type representation theorem for a variety of FL-algebras containing ${\mathcal{B} \mathcal{A} \vee \mathcal{L} \mathcal{G}}$ . 相似文献
16.
Nonlinear mixed-effects (NLME) models remain popular among practitioners for analyzing continuous repeated measures data taken on each of a number of individuals when interest centers on characterizing individual-specific change. Within this framework, variation and correlation among the repeated measurements may be partitioned into interindividual variation and intraindividual variation components. The covariance structure of the residuals are, in many applications, consigned to be independent with homogeneous variances, $ {\sigma}^2{\mathbf{I}}_{n_i} $ , not because it is believed that intraindividual variation adheres to this structure, but because many software programs that estimate parameters of such models are not well-equipped to handle other, possibly more realistic, patterns. In this article, we describe how the programmatic environment within SAS may be utilized to model residual structures for serial correlation and variance heterogeneity. An empirical example is used to illustrate the capabilities of the module. 相似文献
17.
In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 of integral residuated lattices with bottom, which generalize MV-algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor ${{\mathsf{K}^\bullet}}$ , motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV-algebras and the corresponding category ${MV^{\bullet}}$ of monadic MV-algebras induced by “Kalman’s functor” ${\mathsf{K}^\bullet}$ . Moreover, we extend the construction to ?-groups introducing the new category of monadic ?-groups together with a functor ${\Gamma ^\sharp}$ , that is “parallel” to the well known functor ${\Gamma}$ between ? and MV-algebras. 相似文献
18.
We introduce an atomic formula ${\vec{y} \bot_{\vec{x}}\vec{z}}$ intuitively saying that the variables ${\vec{y}}$ are independent from the variables ${\vec{z}}$ if the variables ${\vec{x}}$ are kept constant. We contrast this with dependence logic ${\mathcal{D}}$ based on the atomic formula = ${(\vec{x}, \vec{y})}$ , actually equivalent to ${\vec{y} \bot_{\vec{x}}\vec{y}}$ , saying that the variables ${\vec{y}}$ are totally determined by the variables ${\vec{x}}$ . We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ gives rise to a natural logic capable of formalizing basic intuitions about independence and dependence. We show that ${\vec{y} \bot_{\vec{x}}\vec{z}}$ can be used to give partially ordered quantifiers and IF-logic an alternative interpretation without some of the shortcomings related to so called signaling that interpretations using = ${(\vec{x}, \vec{y})}$ have. 相似文献
19.
Nicholas Long Barbara-Jeanne Austin Mary M. Gound Abesie O. Kelly Adrienne A. Gardner Rick Dunn Stacy B. Harris Kim S. Miller 《Journal of child and family studies》2004,13(1):47-65
The Parents Matter! Program (PMP) has developed three interventions for parents of 4th and 5th grade African-American children (9–12 years old). The overarching goal of all three interventions is to provide parents with knowledge, skills, and support for enhancing their efforts to raise healthy children. The interventions are: (1) Enhanced Communication and Parenting (five 2
-hour sessions), (2) Brief Communication and Parenting (single 2
-hour session), and (3) General Health (single 2
-hour session). This article discusses the development of these interventions, presents an overview of the content of each intervention, and discusses issues related to the facilitation/presentation of these interventions. 相似文献
20.
Action logic of Pratt [21] can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent
to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of
this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action
lattices and the –completeness of the equational theories of action lattices of subsets of a finite monoid and action lattices of binary relations
on a finite universe. We also discuss possible applications in linguistics.
Presented by Jacek Malinowski 相似文献