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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Novometric vs. Log-Linear Model: Intergenerational Occupational Mobility of White American Men

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeling intergenerational occupational mobility (professional and managerial=1; clerical and sales=2; craftsman=3; operatives and laborers=4; farmers=5) using several log-linear model approaches failed to identify a model representing a satisfactory fit of the data (p. 66). For these data an exploratory novometric analysis (constrained by the investigator a priori to obtain stable accuracy in LOO analysis) predicting son’s occupation (class variable) as a function of father’s occupation (multicategorical attribute) identified a parsimonious, relatively strong model.

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ODA vs. Log-Linear Model: Gender and Surgical Operation

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled surgical operation (dummy-coded as 1=neurosurgery; 2=ophthalmology; 3=otorhinolaryngology, 4=vascular-cardiac; 5=thoracic; 6=abdominal; 7=urological; 8=breast; 9=orthopedic; 10=plastic; 11=oral-dental; 12=biopsy) as a function of gender using a log-linear model of: “…quasi-perfect mobility. In this model the main diagonal entries are fixed to their observed values, and the off-diagonal entries are estimated as in a model of quasi-independence” (p. 65). Regardless of the modality of maximum-accuracy analysis used with these data, a single optimal model emerged.

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GenODA Structural Decomposition vs. Log-Linear Model of One-Step Markov Transition Data: Stability and Change in Male Geographic Mobility in 1944-1951 and 1951-1953

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled one-step Markov transition data indicating geographic mobility of American males after WWII, across time, via log-linear analysis. Results revealed: “…most men stayed in their initial regions…but the observed values on the main diagonal are lower in the first matrix, suggesting that the geographic mobility process may not have remained constant over the full period. …Of course, with more than 26,000 cases involved, finding an acceptable fit for anything less than the saturated model is difficult” (p. 56). In this exposition the Gen algorithm is used to conduct structural decomposition analysis (SDA) to identify underlying structural patterns involving stable vs. changing geographic location over time.

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Novometrics vs. ODA vs. Log-Linear Model in Analysis of a Two-Wave Panel Design: Assessing Temporal Stability of Catholic Party Identification in the 1956-1960 SRC Panels

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research used the log-linear model to explain shifts in political party identification (democrat=1; independent=2; republican=3) of 202 Catholic voters who reported party identification in the 1956 and 1960 presidential elections. The results showed: “When the symmetry model is fitted to the six off-diagonal cells…L2=20.99, with df=3, which means we must reject the hypothesis that shifts in each direction tended to cancel each other. …Since 2=15.7 for df=1, we conclude that there is a significant tendency for net change to occur predominantly in one direction. Inspection of the table shows that to be in a Democratic direction. …For the quasi-symmetry hypothesis…L2 =0.12 and df=1. Thus we conclude that the panel data approach symmetry, given unequal marginals in the two years. …The difference in L2 between symmetry and quasi-symmetry models is 20.87 and the difference in df is 2. It is, therefore, reasonable to conclude that the marginal distribution of Catholic voter party identification differs significantly between 1956 and 1960” (pp. 51-54). Exploratory novometric analysis is used to model party identification in 1960 (multicategorical class variable) using party identification in 1956 (multicategorical attribute). Next ODA is used to evaluate temporal stability (confirmatory hypothesis) and to identify statistically reliable instability (exploratory hypothesis) underlying party identification assessed across time.

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Novometric Analysis vs. GenODA vs. Log-Linear Model: Temporal Stability of the Association of Presidential Vote Choice and Party Identification

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled presidential vote (democrat=1; republican=2) as a function of political party identification (democrat=1; independent=2; republican=3) and time (1972=72; 1976=76) via nonsaturated log-linear analysis. Results revealed: “The model {TP}{TV}{PV} has L2=1.88 with df=2. Hence, the best-fitting log-linear model need not include the interaction effect, TPV, thus indicating no significant change in the PV relationship over time… The two bivariate relationships, TP and TV, have substantive interpretations. They indicate that it is the marginal distributions of the vote choice and party identification (within categories of the other variables) which change between times of measurement” (p. 48). Exposition first uses exploratory novometric analysis to model presidenial vote (binary class variable) as a function of political party identification (multicategorical attribute) and time (an ordered attribute). The GenODA algorithm is then used to assess the temporal stability (time is the Gen variable) of the relationship between presidential vote (class variable) and political party identification (categorical attribute).

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Novometric vs. Recursive Causal Analysis: The effect of Age, Education, and Region on Support of Civil Liberties

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled support of another person’s civil liberties (“voted to disallow a Communist speaker”=0; “voted to allow the speaker”=1) as a function of arbitrarily parsed age (39 years=1); education (no college=0; college=1); and region (South, defined as all states in Census South and Border States=1; non-South=0) via log-linear analysis. Results revealed: “The recursive causal model which best represents the data… is the sum of the models for the successive two-, three-, and four-way crosstabulations. The model fits the marginal tables {A}{R}{AR}{RE}{AE}{RS} {AS}{ES} and has L2=3.71 with df=6. …Thus we can see that older persons tend to have lower education, while those living outside the South have a greater chance of some college experience. Odds on holding a tolerant civil liberties attitude are raised by college education and living outside the South but are lower among older persons” (p. 45). Exploratory novometric analysis is used to model support of another’s civil liberties (binary class variable) as a function of region (a categorical at¬tribute), education and age (both treated as ordered attributes measured on categorical ordinal scales).

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Novometrics vs. Yule’s Q: Voter Turnout and Organizational Membership

Paul R. Yarnold

Optimal Data Analysis, LLC

A popular legacy index of association for 2×2 tables that is based on the odds ratio (OR), Yule’s Q=(OR–1)/(OR+1). Yule’s Q ranges between -1.00 and 1.00, with the value 0 indicating no association. Prior research assessing the association between voting behavior (0=not a voter; 1= voter) and the number of one’s organizational memberships (0=no memberships; 1=at least one membership) reported that Q=0.434, and “…the odds of voting among persons belonging to organizations (is) more than 2.5 times greater than the voting odds among those respondents without memberships” (p. 11). These data were analyzed using exploratory novometrics, treating voting behavior as a class variable and number of organizational memberships as an ordered attribute.

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Novometric Analysis Predicting Voter Turnout: Race, Education, and Organizational Membership Status

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled voter turnout (“not voted”=0; “voted”=1) as a function of race (“white”=1; “black”=2), education (“less than high school”=1; “high school graduate”=2; “college”=3), and memberships in organizations (“none”=0; “one or more”=1) via log-linear analysis. Results revealed: “…in the absence of a confirmatory analysis with another sample and in the absence of any compelling theoretical argument for expecting the particular three-variable interaction, (our own preference) would be to choose the more parsimonious model 28, {MER}{MV}{EV}. That model gives a satisfactory fit to the full crosstabulation (L2=4.76, df=5, p<0.45) without resort to a complex three-variable interaction. It also omits the race-turnout effect which is known to be trivial, but which would have to be included in model 34 because it is subsumed in hierarchical relation to the {ERV} term” (p. 40). Exploratory novometric analysis is used to model voter turnout (binary class variable) as a function of race (a categorical attribute), education and number of organizational memberships (both treated as ordered attributes measured on categorical ordinal scales).

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Comparing MMPI-2 F-K Index Normative Data among Male and Female Psychiatric and Head-Injured Patients, Individuals Seeking Disability Benefits, Police and Priest Job Applicants, and Substance Abusers

Paul R. Yarnold

Optimal Data Analysis, LLC

Used as a validity indicator with the MMPI-2, the F-K Index helps to identify people who may over- or under-report psychological issues. Prior research obtained normative data on this index for males and females sampled in a variety of settings, and visual examination of resulting score distributions suggested: “The F-K score distributions appear to differ across the different samples of diagnostic and job applicant samples, as the clinical profiles of these groups would be expected to differ from one another. …Thus, no single set of cutoff scores should be used to judge the motivation or validity of clinical profiles of subjects from different clinical or normative populations” (p. 9). Exploratory novometric analysis is used to predict F-K score as a function of gender and setting in order to establish the existence and assess the strength of the hypothesized inter-sample differences in F-K score distributions.

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Novometrics vs. Polychoric Correlation: Number of Lambs Born Over Two Years

Paul R. Yarnold

Optimal Data Analysis, LLC

This study assesses the agreement between the number of lambs born to 227 ewes over two consecutive years. Polychoric correlation could not be validly used to assess agreement because underlying distributional assumptions were violated. Requiring no such distributional assumptions, prior analysis via ODA identified moderate, statistically significant agreement. Novometric analysis conducted presently identified the globally-optimal model for this application.

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Novometric Analysis vs. MANOVA: MMPI Codetype, Gender, Setting, and the MacAndrew Alcoholism Scale

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research examined scores on the MacAndrew Alcoholism (MAC) scale for three Minnesota Multiphasic Personality Inventory (MMPI) codetypes within three samples: psychiatric inpatients and outpatients; medical outpatients referred for a psychiatric evaluation; and alcoholic inpatients. Analysis via factorial MANOVA revealed: “Mean MAC scores varied drastically as a function of MMPI codetype, gender, and the specific setting in which the MMPI was administered. These large variations in MAC scores suggest that the use of a single cutting score, typically a raw score of 24 or higher, may be inappropriate” (p. 39). These findings obtained by MANOVA are compared with the findings of novometric statistical analysis for this application.

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Using Novometrics to Disentangle Complete Sets of Sign-Test-Based Multiple-Comparison Findings

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior empirical comparison of the timeline follow-back (TLFB, dummy-coded as 1) vs. Drinker Profile (DP, coded as 2) methods of quantifying alcohol consumption in treatment research reported pairwise sign tests comparing these methods separately on four categorical ordinal outcomes: abstinent=1; light=2; moderate=3; heavy=4. It was concluded: “The direction of differences for the abstinent and medium categories approached significance (with unprotected alpha criterion at .05) with the DP more often yielding higher estimates of abstinent days and lower estimates of medium days. The DP significantly more often yielded lower estimates of light days” (p. 27). This example is used to illustrate the use of novometric analysis to disentangle complete sets of sign-test-based pairwise comparison outcomes, including ties.

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