Richard J. Fox

University of Georgia

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Papers

Citation

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i-10 index

Research Field

Modeling Response to Repetitive Promotional Stimuli

Journal of the Academy of Marketing Science (1997)

Richard J. Fox S. K. Reddy Bola Sadashiva Satish Rao

10.1177/0092070397253005

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Citations (10)

Solutions to Empirical Bayes Squared Error Loss Estimation Problems

The Annals of Statistics (1978)

Richard J. Fox

Asymptotically optimal empirical Bayes squared error loss estimation procedures are developed for three families of continuous distributions, uniform $(0, \theta), \theta > 0,$ uniform $\lbrack \theta, \theta + 1), \theta$ arbitrary, and a location parameter family of gamma distributions. The approach taken is to estimate the Bayes estimator directly. However, for the $\lbrack \theta, \theta + 1)$ case, it is shown that the indirect approach of applying the Bayes estimator, versus an almost sure weakly convergent estimator of the prior, also yields an asymptotically optimal procedure.

Bayes estimator

Asymptotically optimal algorithm

Bayes error rate

10.1214/aos/1176344258

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Citations (26)

Book Review

Journal of Marketing Research (1988)

Richard J. Fox

10.1177/002224378802500415

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A Note of Caution Regarding Applying Basic Latent Class Analysis

Ji Hee Song Richard J. Fox

We investigate latent class analysis as a market segmentation method. In particular, we explore the ramifications of the often assumed, perhaps necessarily, local independence condition. Using survey data for a major soft drink brand, we identify brand characteristics which are perceived very differently across simply defined demographic segments. We next apply latent class analysis, assuming local independence, to these same characteristics to derive a segmentation structure. These derived segments, driven by the local independence assumption, are completely different from the initial demographic segments. Strong justification for this assumption, which dictates the solution and cannot be explored in advance, clearly should be present.

Independence

Market Segmentation

Local independence

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Probability Sampling

Wiley International Encyclopedia of Marketing (2010)

Richard J. Fox

Abstract Sampling involves the selection of a subset from a population, and making inferences pertaining to the population based on information from the sample. Probability sampling refers to sampling methods in which chance or randomness is involved in the sample selection process. Each element in the population from which the sample is to be selected has a positive probability of being included in the sample. Probability sampling is the basis for the statistical calculation of the potential error associated with an estimate of a population parameter developed from sample data. Simple random sampling is the most basic form of probability sampling. A simple random sample of size n is selected in such a way that all subsets of size n are equally likely to be the sample selected. The probability that any single item is included in the sample when simple random sampling is used is the ratio of the sample size to the population size. This is the type of sampling that is typically assumed when making basic statistical calculations regarding the precision of sample estimates. For example, the typical 95% confidence interval associated with an estimate is based on the assumption that simple random sampling was used to select the sample. There are more sophisticated forms of probability sampling than simple random sampling, and different statistical calculations are required to determine the precision of estimates when these alternative forms of probability sampling are used. It is obviously important in practice to make sure that the statistical precision calculations are appropriate for the type of probability sampling used.

Poisson sampling

Sample (material)

Probability sampling

Systematic sampling

Sampling distribution

10.1002/9781444316568.wiem02054

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Nonprobability Sampling

Wiley International Encyclopedia of Marketing (2010)

Richard J. Fox

Abstract Sampling involves selecting a subset from a population to analyze for the purpose of gaining information about the population. When the subset is chosen in a manner that does not involve randomness or chance, the method used to select the sample is called a nonprobability sampling method . Estimates derived from such samples may not be representative of the population as a whole. Also, the typical statistical calculations for evaluating the precision of estimates based on the sample are not appropriate when nonprobability sampling is used. In other words, there is no valid margin of error that can be associated with the estimates derived from nonprobability samples. Information derived from nonprobability samples may be useful, but they must be analyzed with caution and a clear understanding of its deficiencies. The most common nonprobability sampling methods are convenience and self‐selecting samples. As the name suggests, a convenience sample refers to a selection process in which the items selected are convenient to the person conducting the survey, such as university professors conducting research using students in their classes. Self‐selecting samples involve situations in which individuals decide to be included in the sample on their own. Telephone or text polls conducted in conjunction with television shows are good examples of self‐selected sampling. Also, the common “suggestion box” survey is a form of self‐selected sampling. A general misconception is that making the sample extremely large compensates for any concerns over the fact that nonprobability sampling was used. No matter how large the sample, if it is selected using nonprobability sampling, concerns regarding how well the sample represents the population are valid. Thousands of people may call in to respond in a telephone poll conducted in conjunction with a television show, but the results are still not necessarily representative of the general public.

Sample (material)

Survey Sampling

10.1002/9781444316568.wiem02049

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Citations (15)

Confirmatory Factor Analysis

Wiley International Encyclopedia of Marketing (2010)

Richard J. Fox

Abstract Confirmatory factor analysis is a statistical technique used when investigating the structure of multivariate data. Each of a set of n observed variables is represented as a linear combination of m ( m < n ) unobserved latent variables or factors, plus an independent error term. The n × n covariance matrix corresponding to the n ‐dimensional observed variables contains the individual variable variances on the diagonal, and the covariances for all pairs of the individual observed variables in the corresponding off‐diagonal positions. A matrix equation, called the covariance equation , relates this n × n covariance matrix to the matrix whose n rows correspond to the coefficients of the m latent factors referred to as factor loadings , and the covariance matrices of the unobserved latent factors and the errors. Confirmatory factor analysis is used to test whether a hypothesized structure is appropriate for multivariate data. The hypothesized structure constrains the matrices appearing in the covariance equation. Individual covariances among the latent factors or among the error terms can be assumed equal or set to zero. Likewise, selected variances (diagonal entries) may be presumed to be equal within each of these matrices. Also, selected factor loadings may be set to zero. A random sample of multivariate observations is used to estimate the corresponding sample covariance matrix with and without the constraints imposed by the hypothesized structure. The “constraint free” covariance matrix is the matrix containing the typical sample descriptive statistics. Maximum likelihood estimation is typically used to determine estimates, with the constraints imposed, of the covariance matrices of the latent factors and errors, and the matrix of factor loadings. A statistical test is conducted to determine whether the hypothesized structure fits the data by comparing the sample covariance matrix to its counterpart produced from the covariance equation using the matrices estimated by maximum likelihood (constraints imposed).

Factor Analysis

Scatter matrix

Matrix (chemical analysis)

Diagonal matrix

10.1002/9781444316568.wiem02060

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Citations (26)

BMDP PC Correspondence Analysis and Unbalanced Repeated Measures Models with Structured Covariance Matrices Supplemental Packages, BMDP PC, Modules CA and 5V, Version 88.2

Journal of Marketing Research (1990)

Richard J. Fox James Lollar

Analysis of covariance

Repeated measures design

10.2307/3172562

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Citations (1)

Velocity damper for electromagnetically levitated materials

OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (1994)

Richard J. Fox

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Access to cerebrospinal fluid absorption sites by infusion into vascular channels of the skull diploë

Journal of neurosurgery (2007)

Kelly Johnston Anil H. Walji Richard J. Fox Jeffrey A. Pugh Keith Aronyk

Object The purpose of this human cadaver study was to determine whether or not an intraosseous skull infusion would access the superior sagittal sinus (SSS) via intradural venous channels. The diploic space of the skull bone contains a sinusoidal vascular network that communicates with the underlying dura mater. Diploic veins in the parasagittal area connect with endothelium-lined intradural channels in the subjacent dura and ultimately with the dural venous sinuses. A significant proportion of cerebrospinal fluid (CSF) absorption is thought to occur via arachnoid granulations in the region of the SSS and especially along the parasagittal dura where arachnoid granulations are surrounded by intradural venous channels (lateral lacunae). The CSF is likely to be conducted from the subarachnoid space into the venous system via the fine intradural channels making up the lateral lacunae. Methods Infusion of vinyl acetate casting material into the diploic space of the human cadaveric skull resulted in complete filling of the lateral lacunae and SSS. Corrosion casting techniques and examination under magnification were used to characterize the anatomical connections between diploic spaces and dural venous sinuses. Results Corrosion casting, performed on five formalin-fixed cadavers, clearly showed the anatomical connections between the diploic infusion site and the venous sinuses in the underlying parasagittal dura where some of the CSF is thought to be absorbed. Conclusions The diploic vascular channels of the human skull may represent an indirect pathway into the dural venous sinuses. Intraosseous skull infusion may represent another possible strategy for diversion of CSF into the vascular system in the treatment of hydrocephalus.

Dural venous sinuses

Subarachnoid space

Cadaveric spasm

Sinus (botany)

Calvaria

10.3171/jns.2007.107.4.841

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