Complete Lω1,ω‐sentences with maximal models in multiple cardinalities

2019 ◽  
Vol 65 (4) ◽  
pp. 444-452 ◽  
Author(s):  
John Baldwin ◽  
Ioannis Souldatos
Keyword(s):  
Maximal Models

scholarly journals Toward categoricity for classes with no maximal models

1999 ◽  
Vol 97 (1-3) ◽  
pp. 1-25 ◽  
Author(s):  
Saharon Shelah ◽  
Andrés Villaveces
Keyword(s):  
Maximal Models

Generating all maximal models of a Boolean expression

2000 ◽  
Vol 74 (3-4) ◽  
pp. 157-162 ◽  
Author(s):  
Dimitris J. Kavvadias ◽  
Martha Sideri ◽  
Elias C. Stavropoulos
Keyword(s):  
Boolean Expression ◽  
Maximal Models

scholarly journals When fixed and random effects mismatch: Implications for model comparisons

2021 ◽  
Author(s):  
João Veríssimo
Keyword(s):  
Random Effects ◽  
Model Comparison ◽  
Mixed Effects ◽  
Mixed Effects Models ◽  
Complex Case ◽  
Model Comparisons ◽  
Fixed And Random Effects ◽  
Assessment Of Evidence ◽  
Correlated Predictors ◽  
Maximal Models

Mixed-effects models containing both fixed and random effects have become widely used in the cognitive sciences, as they are particularly appropriate for the analysis of clustered data. However, testing hypotheses in the presence of random effects is not completely straightforward, and a set of best practices for statistical inference in mixed-effects models is still lacking. Van Doorn et al. (2021) investigated how Bayesian hypothesis testing in mixed-effects models is impacted by particular model specifications. Here, we extend their work to the more complex case of models with three-level factorial predictors and, more generally, with multiple correlated predictors. We show how non-maximal models with correlated predictors contain 'mismatches' between fixed and random effects, in which the same predictor can refer to different effects in the fixed and random parts of a model. We then demonstrate though a series of Bayesian model comparisons that such mismatches can lead to inaccurate estimations of random variance, and in turn to biases in the assessment of evidence for the effect of interest. We present specific recommendations for how researchers can resolve mismatches or avoid them altogether: by fitting maximal models, eliminating correlations between predictors, or by residualising the random effects. Our results reinforce the observation that model comparisons with mixed-effects models can be surprisingly intricate and highlight that researchers should carefully and explicitly consider which hypotheses are being tested by each model comparison. Data and code are publicly available in an OSF repository at https://osf.io/njaup.

A note on Σ1-maximal models

2007 ◽  
Vol 72 (3) ◽  
pp. 1072-1078 ◽  
Author(s):  
A. Cordón-Franco ◽  
A. Fernández-Margarit ◽  
F.F. Lara-Martín
Keyword(s):  
First Order ◽  
Recursive Theory ◽  
Order Arithmetic ◽  
Maximal Models

AbstractLet T be a recursive theory in the language of first order Arithmetic. We prove that if T extends: (a) the scheme of parameter free Δ1-minimization (plus exp). or (b) the scheme of parameter free Π1-induction, then there are no Σ1-maximal models with respect to T. As a consequence, we obtain a new proof of an unpublished theorem of Jeff Paris stating that Σ1-maximal models with respect to IΔ0 + exp do not satisfy the scheme of Σ1-collection BΣ1.

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