1,954 research outputs found
Derivative Computations and Robust Standard Errors for Linear Mixed Effects Models in lme4
While robust standard errors and related facilities are available in R for
many types of statistical models, the facilities are notably lacking for models
estimated via lme4. This is because the necessary statistical output, including
the Hessian and casewise gradient of random effect parameters, is not
immediately available from lme4 and is not trivial to obtain. In this article,
we supply and describe two new functions to obtain this output from Gaussian
mixed models: estfun.lmerMod() and vcov.full.lmerMod(). We discuss the
theoretical results implemented in the code, focusing on calculation of robust
standard errors via package sandwich. We also use the Sleepstudy data to
illustrate the code and compare it to a benchmark from package lavaan.Comment: Accepted at Journal of Statistical Softwar
Generalized Measurement Invariance Tests with Application to Factor Analysis
The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we construct tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (1) isolating specific parameters affected by measurement invariance violations, and (2) identifying subgroups of individuals that violated measurement invariance based on a continuous auxiliary variable. The tests are presented and illustrated in detail, along with simulations examining the tests' abilities in controlled conditions.measurement invariance, parameter stability, factor analysis, structural equation models
Bayesian comparison of latent variable models: Conditional vs marginal likelihoods
Typical Bayesian methods for models with latent variables (or random effects)
involve directly sampling the latent variables along with the model parameters.
In high-level software code for model definitions (using, e.g., BUGS, JAGS,
Stan), the likelihood is therefore specified as conditional on the latent
variables. This can lead researchers to perform model comparisons via
conditional likelihoods, where the latent variables are considered model
parameters. In other settings, however, typical model comparisons involve
marginal likelihoods where the latent variables are integrated out. This
distinction is often overlooked despite the fact that it can have a large
impact on the comparisons of interest. In this paper, we clarify and illustrate
these issues, focusing on the comparison of conditional and marginal Deviance
Information Criteria (DICs) and Watanabe-Akaike Information Criteria (WAICs) in
psychometric modeling. The conditional/marginal distinction corresponds to
whether the model should be predictive for the clusters that are in the data or
for new clusters (where "clusters" typically correspond to higher-level units
like people or schools). Correspondingly, we show that marginal WAIC
corresponds to leave-one-cluster out (LOcO) cross-validation, whereas
conditional WAIC corresponds to leave-one-unit out (LOuO). These results lead
to recommendations on the general application of the criteria to models with
latent variables.Comment: Manuscript in press at Psychometrika; 31 pages, 8 figure
Testing non-nested structural equation models
In this paper, we apply Vuong's (1989) likelihood ratio tests of non-nested
models to the comparison of non-nested structural equation models. Similar
tests have been previously applied in SEM contexts (especially to mixture
models), though the non-standard output required to conduct the tests has
limited their previous use and study. We review the theory underlying the tests
and show how they can be used to construct interval estimates for differences
in non-nested information criteria. Through both simulation and application, we
then study the tests' performance in non-mixture SEMs and describe their
general implementation via free R packages. The tests offer researchers a
useful tool for non-nested SEM comparison, with barriers to test implementation
now removed.Comment: 24 pages, 6 figure
Certificate Transparency with Enhancements and Short Proofs
Browsers can detect malicious websites that are provisioned with forged or
fake TLS/SSL certificates. However, they are not so good at detecting malicious
websites if they are provisioned with mistakenly issued certificates or
certificates that have been issued by a compromised certificate authority.
Google proposed certificate transparency which is an open framework to monitor
and audit certificates in real time. Thereafter, a few other certificate
transparency schemes have been proposed which can even handle revocation. All
currently known constructions use Merkle hash trees and have proof size
logarithmic in the number of certificates/domain owners.
We present a new certificate transparency scheme with short (constant size)
proofs. Our construction makes use of dynamic bilinear-map accumulators. The
scheme has many desirable properties like efficient revocation, low
verification cost and update costs comparable to the existing schemes. We
provide proofs of security and evaluate the performance of our scheme.Comment: A preliminary version of the paper was published in ACISP 201
Faith Transformed : Christian Encounters with Jews and Judaism
Traditionally, Christian churches have taught that the validity of Judaism came to an end with the emergence of Christianity. But in the last half-century, many Christians have repudiated this teaching and have affirmed the abiding validity of Judaism. Consequently, they have had to reevaluate Christian self-understanding in relation to Judaism. In Faith Transformed, Christian scholars who have been at the forefront of Christian-Jewish relations share how their encounters with Jews and Judaism have transformed their understanding and practice of Christianity. They reveal how their Christian faith has been profoundly enriched by drawing inspiration from the Jewish tradition.https://digitalcommons.csbsju.edu/theology_books/1005/thumbnail.jp
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