A Computational Study Assessing Maximum Likelihood and Noniterative Methods for Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models

Beh, Eric J.; Farver, Thomas B

doi:10.5402/2012/396831

Cited by 3 publications

(7 citation statements)

References 11 publications

(45 reference statements)

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“…From Tables 1 to 6, it can be seen that and , given by (2.2) and (2.3), provide estimates which are close to each other. The BDNI estimator underestimates the linear-by-linear association; confirming the findings of computational studies carried out by Beh and Farver (2012a, b, Zafar et al, 2013a, 2015. However, earlier Beh and Farver (2012a,b) showed using the Wald test that the BDNI and LogNI estimates are statistically similar to the estimates obtained by the Newton -Raphson method.…”

Section: Data and Designsupporting

confidence: 83%

Modelling risk profiles of depression symptoms using Cloninger's temperament and character traits: a non-iterative approach to assess linear-by-linear association within ordered contingency tables

Zafar¹,

Hudson²,

Beh³

et al. 2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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Personality is linked to mental illness. The relationship between the seven temperament and character traits (TCIs), (Novelty seeking (NS), Harm Avoidance (HA), Reward Dependence (RD), Persistence (P), Self-directedness (S), Cooperativeness (C) and Self Transcendence (ST)), of Cloninger (1994) and three symptoms of psychological distress, or SCLs (Depression (D), Anxiety (A) and Psychoticism (Psy)) is investigated across gender and shown to have significantly different symptom profiles post treatment. The data used in this study was earlier analysed by Turner, et al. (2003) and comes from patients measured pre and post-treatment from the NZ Christchurch Psychotherapy of Depression Study (Joyce, et al. 2002). In this study we have used the newly developed direct estimation approach (Beh and Davy, 2004 and Zafar et al., 2015) to estimate the linear-by-linear association in two-way tables, within the framework of ordinal log-linear models (OLLMs), with the aim of analysing associations between the TCIs and SCLs. Two non-iterative estimators were considered for this study-the Beh-Davy non-iterative estimator (BDNI) (Beh and Davy, 2004) and the Log non-iterative estimator (LogNI) (Beh and Farver, 2009). The BDNI and LogNI estimation methods provide closed-form estimators which do not require iteration to estimate the linear-by-linear association parameter of OLLMs, unlike their conventional and iterative counter parts, such as the Newton-Raphson and the iterative proportional fitting methods. The estimates obtained from the BDNI and LogNI estimation methods are reported, for pairwise relationships between TCIs and symptoms, along with the standard errors and p-values for males and females for pre and post treatment. Both estimators, BDNI and LogNI, provide estimates which are close to each other. We found significant changing relationships between the seven TCIs and psychological distress symptoms across gender for NS and P post treatment; with both TCIs and SCLs dichotomised by the median. We found statistically significant differences between the BDNI and LogNI estimates for males and females, post-treatment; establishing that higher levels of NS are associated with less D and Psy in males as compared to females. Higher HA is shown to be associated with higher D, A and Psy in males and females, pre and post-treatment. S is found to be negatively related to D, A and Psy for males and in females, pre and posttreatment. P is demonstrated as gender-specific only in the case of D; with less D associated with higher levels of P in males comparison with females post treatment. In addition, we demonstrate the linear-by-linear association between pre-treatment TCI's and change in depression, anxiety and psychoticism (ΔD, ΔA and ΔPsy), where the change is defined as categorised by the median scores of the (post-pre-treatment) levels. We show that pairwise association between three TCI's (HA, P and C) and two of our three symptoms of psychological distress, ΔD and ΔPsy, are gender-specific. These results reported agree, in par...

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Section: Data and Designsupporting

confidence: 83%

Modelling risk profiles of depression symptoms using Cloninger's temperament and character traits: a non-iterative approach to assess linear-by-linear association within ordered contingency tables

Zafar¹,

Hudson²,

Beh³

et al. 2015

Weber, T., McPhee, M.J. And Anderssen, R.S. (Eds) MODSIM2015, 21st International Congress on Modelling and Simulation

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“…To evaluate the performance and compare the non-iterative estimates of ϕ using (2) and (3)-and two additional Taylor-series approximations of (2)-with the estimates obtained using the iterative algorithm of Newton's method, [42,43] performed a series of simulation studies. As part of their studies, strategies needed to be considered for dealing with the presence of random zero-cell frequencies since the logarithm function in (2) leads to non-existent solutions for such cases.…”

Section: Non-iterative Estimation Of the Linear-by-linear Association...mentioning

confidence: 99%

“…See, for example, [3] (Section 10.6.5), [23] (p. 119) and [58][59][60][61] for a discussion of this issue. In the simulations below, we shall be replacing a zero-cell frequency with 0.05, as [42][43][44] did. Note that determining φBDNI when random zero-cell frequencies are present does not suffer from this problem.…”

Section: Non-iterative Estimation Of the Linear-by-linear Association...mentioning

confidence: 99%

“…With the foundational mathematical links between the non-iterative estimates of the linear-by-linear association parameter established, and their reliability and stability verified through simulation, this paper identifies the asymptotic characteristics of the two key non-iterative estimates studied [40][41][42][43][44]. We shall be paying particular attention to the bias of the estimators-a topic that was briefly examined by [45].…”

Section: Introductionmentioning

confidence: 97%

“…The former authors propose one method for estimating the linear-bylinear parameter through non-iterative (direct) means, while the latter authors considered three further, and related, methods. The accuracy and reliability of the non-iterative estimation for the OLLM of a doubly ordered contingency table was investigated by [42,43], who provided a simulation study of these four methods. They demonstrated that using their non-iterative techniques provides exceptionally stable and reliable estimates of the linear-by-linear association parameter when compared with Newton's method.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Characteristics of the Non-Iterative Estimates of the Linear-by-Linear Association Parameter for Ordinal Log-Linear Models

et al. 2022

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Over the past decade, a series of procedures has been introduced to estimate, using a non-iterative method, the linear-by-linear association parameter of an ordinal log-linear model. This paper will examine the two key non-iteratively determined estimates of the parameter for the analysis of the association between the two categorical variables that form a contingency table; these are the log and the Beh-Davy non-iterative estimates, referred to simply as the LogNI and the BDNI estimates, respectively. Such an examination will focus on determining their asymptotic characteristics. To do so, a computational study was undertaken for tables of varying sizes to show that these two estimates are asymptotically unbiased. It is also shown that both estimates are asymptotically normally distributed. On the basis of the standard errors, their relative efficiency was established for the 13 commonly analysed contingency tables that appear throughout the literature.

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Linking ordinal log-linear models with Correspondence Analysis: an application to estimating drug-likeness in the drug discovery process

Zafar

Cheema²,

Beh³

et al. 2013

Piantadosi, J., Anderssen, R.S. And Boland J. (Eds) MODSIM2013, 20th International Congress on Modelling and Simulation

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Ordinal log-linear models (OLLM's) are amid the most widely used and powerful techniques to model association among ordinal variables in categorical data analysis. The parameters of such models are traditionally estimated using iterative algorithms, such as the Newton-Raphson method and iterative proportional fitting. More recent advances involve a non-iterative estimation method that performs equally well for estimation of the linear-by-linear association in OLLM's for a two-way table. This paper establishes a link between the Beh-Davy non-iterative estimation method (BDNI) (Beh & Davy, 2003) and the well-known ordinal correspondence analysis (CA) technique for two dimensional tables. The BDNI estimator of association relies on orthogonal polynomials (OP's), an approach dating from Lancaster (1953) to Beh and Davy (2003). OP's provide insight into the origin and development of non-iterative estimation in OLLM's, as an alternative to popular iterative procedures. The main advantage of OP's is that the resultant parameters enable estimation of the linear, and also quadratic and higher order association structures amongst the ordered categories. Ordinal CA was first introduced by Beh (1997). We compare the linear-by-linear BDNI association procedure with the linear-by-linear association method depicted via graphical representation in ordinal CA. To demonstrate this link and theory we analyzed the relationships between predictors of drug-likeness used in drug discovery to filter out small molecule (drugs) that may fail clinical trials. In vitro absorption, distribution, metabolism and elimination (ADME) assays are now being conducted throughout the drug discovery process, from hit to lead optimization (Kerns & Li, 2008). The analytical community needs still to develop faster and better analytic methods to enhance the 'developability' of drug leads, and to formalize strategies for ADME assessment of candidates in the discovery and pre-clinical stages (Kassel 2004). Assessing drug-likeness depends on the nature of relationships between surrogate measures of drug-likeness (aqueous solubility, permeability) and physicochemical properties (lipophilicity, molecular weight (MW)). To date, lipophilicity is expressed quantitatively as logP, the most popular predictor for permeation. We apply our methods to test rules of druggability (Lipinski 2000). In this study 1,279 small molecules from Hudson et al. (2012), based on the DrugBank3.0 database (Knox et al., 2011), a unique chem-informatics resource are analysed. The pair-wise association between categorised variants of 2 of the 4 traditional parameters of Lipinski's rule of five (Ro5), namely MW and logP, and an additional parameter, polar surface area (PSA), introduced by Veber et al., (2002), are shown to differ in magnitude or swap sign across strata, where strata are defined by a molecule's druggable (Ro5 compliant) versus non-druggable (Ro5 violation) status. Log P's association with MW, assumed to be positive, is shown to: [1] change sign from significantly negative t...

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A Computational Study Assessing Maximum Likelihood and Noniterative Methods for Estimating the Linear-by-Linear Parameter for Ordinal Log-Linear Models

Cited by 3 publications

References 11 publications

Modelling risk profiles of depression symptoms using Cloninger's temperament and character traits: a non-iterative approach to assess linear-by-linear association within ordered contingency tables

Modelling risk profiles of depression symptoms using Cloninger's temperament and character traits: a non-iterative approach to assess linear-by-linear association within ordered contingency tables

Asymptotic Characteristics of the Non-Iterative Estimates of the Linear-by-Linear Association Parameter for Ordinal Log-Linear Models

Linking ordinal log-linear models with Correspondence Analysis: an application to estimating drug-likeness in the drug discovery process

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