Novometric Analysis of Transition Matrices to Ascertain Markovian Order

Paul R. Yarnold

Optimal Data Analysis, LLC

The American National Election Panel Study modeled transitions in social class identification occurring between 1956, 1958, and 1960. Visual analysis suggested “…that transition probabilities linking class identifications in 1958 and 1960 vary with 1956 identification”. Transition tables were compared using Goodman’s chi-square procedure: chi-square=98.2, df=2, p<0.0001. Based on visual examination and non-disentangled omnibus chi-square findings, the null hypothesis of a first-order Markov model was rejected in favor of the alternative hypothesis that the underlying temporal process is a second-order Markovian (pp. 13-15). In contrast, novometric analysis indicated that a first-order Markov model is appropriate for these data.

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Novometrics vs. ODA: Work Shift and Raw Material Production Quality

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research used ODA to identify the association between work shift (multicategorical class variable, dummy-coded as 1, 2, 3) and the quality of raw material produced (ordered attribute consisting of the integers 1-6). The model obtained using ODA is compared with a novometric model obtained for the same data.

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Novometric vs. Log-Linear Analysis: Church Attendance, Age and Religion

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research using log-linear analysis to model church attendance (1=low; 2=medium; 3=high) as a function of age (young=0; old=1) and religion (non-Catholic=0; Catholic=1) found that the best fitting model {AR}{AC}{RC} had L2=7.25, df=2, indicating insufficient badness-of-fit (pp. 67-69). For these data exploratory novometric analysis predicting church attendance (ordered class variable) using religion (categorical attribute) and age (ordered attribute) identified a parsimonious, relatively weak model with stable classification training and LOO performance.

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Novometric vs. Logit Analysis: Abortion Attitude by Religion and Time

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research using logit analysis to model abortion attitude (oppose=0; favor=2) as a function of religion (Protestant=1; Catholic=2; Jewish=3; Other=4) and time (1972=72; 1978=78) found: “The best fitting model…has separate effects for being Catholic or non-Catholic and for being Protestant or non-Protestant. The categories of Jewish and Other have no separate effects and are implicitly grouped or collapsed together. The result is a religious trichotomy. …The odds on a favorable response are identical in both years: .89 for Protestants, .64 for Catholics, and 3.44 for Jews and Others” (pp. 70-72). For these data exploratory novometric analysis predicting abortion attitude (class variable) as a function of religion (multicategorical attribute) and time (ordered attribute) identified a parsimonious, relatively weak model with stable classification training and LOO performance.

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Novometric vs. Logit vs. Probit Analysis: Using Gender and Race to Predict if Adolescents Ever Had Sexual Intercourse

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled if adolescents ever had sexual intercourse (the dependent variable: yes=1, no=0) using main-effect logit and probit analysis models treating gender (female=0, male=1) and race (“white” =1; “black”=2) as the independent variables. Both models identified statistically significant effects for gender and race, and both models misclassified all observations that had sexual intercourse: ESS=0. In exploratory novometric analysis conducted for these data a statistically significant, cross-generalizable race effect emerged that yielded moderate ESS=25.25, p<0.001.

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