An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials

Koehler, Kenneth J.; Larntz, Kinley

doi:10.2307/2287455

Cited by 122 publications

(104 citation statements)

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“…Note that p -values are not reported for the test statistics in these models because the degrees of freedom (df) are large (df≥99 for each model). Large models suffer from sparseness in the observed data table; when data are sparse it has been shown that the distribution of the G 2 does not follow a chi-square distribution (Koehler, 1986; Koehler & Larntz, 1980). Lower AIC and BIC values reflect an optimal balance between model fit and parsimony.…”

Section: Resultsmentioning

confidence: 99%

Latent Transition Analysis: Benefits of a Latent Variable Approach to Modeling Transitions in Substance Use

Lanza¹,

Patrick²,

Maggs³

2010

Journal of Drug Issues

192

143

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We apply latent transition analysis (LTA) to characterize transitions over time in substance use behavior profiles among first-year college students. Advantages of modeling substance use behavior as a categorical latent variable are demonstrated. Alcohol use (any drinking and binge drinking), cigarette use, and marijuana use were assessed in a sample (N=718) of college students during the fall and spring semesters. Four profiles of 14-day substance use behavior were identified: (1) Non-Users; (2) Cigarette Smokers; (3) Binge Drinkers; and (4) Bingers with Marijuana Use. The most prevalent behavior profile at both times was the Non-Users (with over half of the students having this profile), followed by Binge Drinkers and Bingers with Marijuana Use. Cigarette Smokers was the least prevalent behavior profile. Gender, race/ethnicity, early onset of alcohol use, grades in high school, membership in the honors program, and friendship goals were all significant predictors of substance use behavior profile. Keywords latent transition analysis; college students; substance useThe transition to college is associated with increases in heavy alcohol use (White et al., 2006) and marijuana use (Fromme, Corbin, & Kruse, 2008). Students who attend college engage in more binge drinking (i.e., consuming five or more alcoholic drinks in a row in the past 2 weeks) and have a higher prevalence of annual and 30-day alcohol use, but do not evidence elevated levels of cigarette, marijuana, or cocaine use compared to their same-age peers who do not attend college (O'Malley & Johnston, 2002). Approximately 40% of college students engage in binge drinking in a 14-day period (O'Malley & Johnston, 2002), and this behavior is associated with well-documented negative consequences (e.g., Hingson, Heeren, Winter, & Wechsler, 2005;Jackson, Sher, & Park, 2006). In addition, college students' tobacco use continues to be a concern, although smoking is less prevalent among college attenders than among non-attenders (Tercyzk, Rodriguesz, & Audrain-McGovern, 2007). Cannabis (i.e., marijuana) use among college students is also associated with substance use disorders and other negative use-related consequences (Caldeira, Arria, O'Grady, Vincent, & Wish, 2008). However, much less research has considered patterns of college students' use of multiple substances and the public health importance of the intersection of these behaviors. A better understanding of substance use behavior and negative consequences and their predictors among college students requires a more holistic NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript treatment of behavior, where use of multiple substances is considered simultaneously. The current study takes a person-centered approach to modeling behavior; we demonstrate the advantages of using latent transition analysis (LTA) to describe behavioral profiles characterized by profiles of alcohol use, binge drinking, cigarette use, and marijuana use across the first year of college. Transitions in subst...

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Section: Resultsmentioning

confidence: 99%

Latent Transition Analysis: Benefits of a Latent Variable Approach to Modeling Transitions in Substance Use

Lanza¹,

Patrick²,

Maggs³

2010

Journal of Drug Issues

192

143

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“…Furthermore, the number of communities involved tends to produce a table with a larger number of rows than is typical of a cross-tabulation table in most analytical applications. One early paper suggests that χ 2 may still function adequately with low frequencies of observations, although perhaps with a correction (i.e., using df = k - 2 instead of k - 1) [33]. More work may be required to adequately assess how well

I_{P}^{2}

functions with zero counts, and it may possibly need to be adjusted using two stage models [34], mixture models [35], or a generalized Poisson distribution [36].…”

Section: Discussionmentioning

confidence: 99%

Assessing community variation and randomness in public health indicators

Arndt

Ación

Caspers

et al. 2011

Popul Health Metrics

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BackgroundEvidence-based health indicators are vital to needs-based programming and epidemiological planning. Agencies frequently make programming funds available to local jurisdictions based on need. The use of objective indicators to determine need is attractive but assumes that selection of communities with the highest indicators reflects something other than random variability from sampling error.MethodsThe authors compare the statistical performance of two heterogeneity measures applied to community differences that provide tests for randomness and measures of the percentage of true community variation, as well as estimates of the true variation. One measure comes from the meta-analysis literature and the other from the simple Pearson chi-square statistic. Simulations of populations and an example using real data are provided.ResultsThe measure based on the simple chi-square statistic seems superior, offering better protection against Type I errors and providing more accurate estimates of the true community variance.ConclusionsThe heterogeneity measure based on Pearson's χ2 should be used to assess indices. Methods for improving poor indices are discussed.

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“…If that number is approaching zero for at least one cell, then we can expect that the statistic will behave aberrantly. For instance, [9] cites research showing that the asymptotic behavior of

X_{n}^{2}

is not as expected, giving some explanation for the well-known rule of thumb of having at least five as the expected count in each cell (though subsequent work has shown this particular cutoff to be conservative [10]).…”

Section: Bin Selection For Xn2mentioning

confidence: 99%

The choice of the number of bins for the statistic

White

Bonetti

Pagano

2009

Computational Statistics & Data Analysis

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Methods to monitor spatial patterns of disease in populations are of interest in public health practice. The M statistic uses interpoint distances between cases to detect abnormalities in the spatial patterns of diseases. This statistic compares the observed distribution of interpoint distances with that which is expected when no unusual spatial patterns exist. We show the relationship of M to Pearson's Chi Square statistic, . Both statistics require the discretization of continuous data into bins and then are formed by creating a quadratic form, scaled by an appropriate variance covariance matrix. We seek to choose the number and type of these bins for the M statistic so as to maximize the power to detect spatial anomalies. By showing the relationship between M to , we argue for the extension of the theory that has been developed for the selection of the number and type of bins for to M. We further show that spatial data provides a unique insight into the problem through examples with simulated data and spatial data from a health care provider. In the spatial setting, these indicate that the optimal number of bins depends on the size of the cluster. For large clusters, a smaller number of bins appears to be preferrable, however for small clusters having many bins increases the power. Further, results indicate that the number of bins does not appear to vary with m, the number of spatial locations. We discuss the implications of this result for further work.

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An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials

Cited by 122 publications

References 0 publications

Latent Transition Analysis: Benefits of a Latent Variable Approach to Modeling Transitions in Substance Use

Latent Transition Analysis: Benefits of a Latent Variable Approach to Modeling Transitions in Substance Use

Assessing community variation and randomness in public health indicators

The choice of the number of bins for the statistic

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