82,812 research outputs found
How Good are Our Measures? Investigating the Appropriate Use of Factor Analysis for Survey Instruments
Background: Evaluation work frequently utilizes factor analysis to establish the dimensionality, reliability, and stability of surveys. However, survey data is typically ordinal, violating the assumptions of most statistical methods, and thus is often factor-analyzed inappropriately. Purpose: This study illustrates the salient analytical decisions for factor-analyzing ordinal survey data appropriately and demonstrates the repercussions of inappropriate analyses. Setting: The data used for this study are drawn from an evaluation of the efficacy of a drama-based approach to teaching Shakespeare in elementary and middle school. Intervention: Not applicable. Research Design: Survey research. Data Collection and Analysis: Four factor analytic methods were compared: a traditional exploratory factor analysis (EFA), a full-information EFA, and two EFAs within the confirmatory factor analysis framework (E/CFA) conducted according to the Jöreskog method and the Gugiu method. Findings: Methods appropriate for ordinal data produce better models, the E/CFAs outperform the EFAs, and the Gugiu method demonstrates greater model interpretability and stability than the Jöreskog method. These results suggest that the Gugiu E/CFA may be the preferable factor analytic method for use with ordinal data. Practical applications of these findings are discussed. Keywords: factor analysis; ordinal data; E/CFA; survey research
Analysis-of-marginal-Tail-Means (ATM): a robust method for discrete black-box optimization
We present a new method, called Analysis-of-marginal-Tail-Means (ATM), for
effective robust optimization of discrete black-box problems. ATM has important
applications to many real-world engineering problems (e.g., manufacturing
optimization, product design, molecular engineering), where the objective to
optimize is black-box and expensive, and the design space is inherently
discrete. One weakness of existing methods is that they are not robust: these
methods perform well under certain assumptions, but yield poor results when
such assumptions (which are difficult to verify in black-box problems) are
violated. ATM addresses this via the use of marginal tail means for
optimization, which combines both rank-based and model-based methods. The
trade-off between rank- and model-based optimization is tuned by first
identifying important main effects and interactions, then finding a good
compromise which best exploits additive structure. By adaptively tuning this
trade-off from data, ATM provides improved robust optimization over existing
methods, particularly in problems with (i) a large number of factors, (ii)
unordered factors, or (iii) experimental noise. We demonstrate the
effectiveness of ATM in simulations and in two real-world engineering problems:
the first on robust parameter design of a circular piston, and the second on
product family design of a thermistor network
Social Welfare in One-sided Matching Markets without Money
We study social welfare in one-sided matching markets where the goal is to
efficiently allocate n items to n agents that each have a complete, private
preference list and a unit demand over the items. Our focus is on allocation
mechanisms that do not involve any monetary payments. We consider two natural
measures of social welfare: the ordinal welfare factor which measures the
number of agents that are at least as happy as in some unknown, arbitrary
benchmark allocation, and the linear welfare factor which assumes an agent's
utility linearly decreases down his preference lists, and measures the total
utility to that achieved by an optimal allocation. We analyze two matching
mechanisms which have been extensively studied by economists. The first
mechanism is the random serial dictatorship (RSD) where agents are ordered in
accordance with a randomly chosen permutation, and are successively allocated
their best choice among the unallocated items. The second mechanism is the
probabilistic serial (PS) mechanism of Bogomolnaia and Moulin [8], which
computes a fractional allocation that can be expressed as a convex combination
of integral allocations. The welfare factor of a mechanism is the infimum over
all instances. For RSD, we show that the ordinal welfare factor is
asymptotically 1/2, while the linear welfare factor lies in the interval [.526,
2/3]. For PS, we show that the ordinal welfare factor is also 1/2 while the
linear welfare factor is roughly 2/3. To our knowledge, these results are the
first non-trivial performance guarantees for these natural mechanisms
A Bayesian semiparametric latent variable model for mixed responses
In this article we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric predictor. We extend existing LVM with simple linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply our approach to a large German social science survey which motivated our methodological development
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