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At least 19 recordsLinked to original sources
PubMed2002

Kinetic analysis of thermal decomposition for penicillin sodium salts: model-fitting and model-free methods.

A kinetic study on decomposition processes of some penicillin salts was carried out. Both isothermal and dynamic thermogravimetric curves were used. As expected by their complex structures, several steps with different energies were involved in decomposition processes. Model-fitting and -free kinetic approaches were applied to nonisothermal and isothermal data. The kinetic triplet (f(alpha),A and E(a)) related to model-fitting method that defines a single step reaction resulted to be at variance with the multi-step nature of salts-decomposition. The model-free approach represented by the isothermal and nonisothermal isoconversional methods, gave different dependencies of the activation energy on the extent of conversion. The complex nature of the multi-step process of the studied compounds was more easily revealed using a broader temperature range in nonisothermal isoconversional method. The failure in the model-fitting method did not allow calculating shelf life and half-life times.

Ampicillin↗
PubMed2003

Crystallization kinetics of amorphous nifedipine studied by model-fitting and model-free approaches.

The crystallization of amorphous nifedipine was studied using hot-stage microscopy (HSM), powder X-ray diffractometry (PXRD), and differential scanning calorimetry (DSC). The kinetic data obtained from DSC studies under isothermal and nonisothermal conditions were examined using both model-fitting and model-free approaches. Evaluation of 16 different models showed that model A4 (Avrami-Erofeev, n = 4) to be most appropriate for crystallization in the conversion range 0.05-0.80. This choice was based on the goodness of fit, the residual plots, and the guidance provided by the model-free approach. The model-free approach indicated that the activation energy decreases slightly as the crystallization proceeds. This variation of the activation energy with the extent of conversion determines the range of conversion over which a model can be fit, and the magnitude of the activation energy helps in the selection of the best model. The model-free approach gives much better predictions than the model of best fit and allows the experimental kinetic function to be numerically evaluated. At the early stage (alpha = 0-0.6), the numerically reconstructed model is almost identical to A4, but gradually approaches A3 (Avrami-Erofeev, n = 3) as the crystallization progresses (alpha = 0.6-0.8) and deviates from both models near the end of the reaction. This behavior may be explained by the relative contributions of nucleation and crystal growth at different stages of the reaction.

Calorimetry, Differential Scanning↗
PubMed2003

Potential problems with "well fitting" models.

The assessment of model fit is a more complex and indeterminate process than is commonly acknowledged by researchers who use structural equation modeling (SEM) techniques. Even models that are well fitting according to commonly used statistical tests and descriptive fit indices can have significant problems and ambiguities. The authors discuss 7 potential difficulties that can arise and that should temper researchers' conclusions: equivalent models, nonequivalent but well-fitting alternative models, omitted variables, problematic lower-order model components, the failure to parse composite models into meaningful partitions (e.g., measurement vs. structural), inattention to the multiple factors that affect the sensitivity of measures of fit to model misspecifications, and reliance on specification searches. In addition to providing examples of each of these problems, the authors offer recommendations for psychopathologists who conduct SEM analyses.

Analysis of Variance↗
PubMed2001

Selecting the best-fit model of nucleotide substitution.

Despite the relevant role of models of nucleotide substitution in phylogenetics, choosing among different models remains a problem. Several statistical methods for selecting the model that best fits the data at hand have been proposed, but their absolute and relative performance has not yet been characterized. In this study, we compare under various conditions the performance of different hierarchical and dynamic likelihood ratio tests, and of Akaike and Bayesian information methods, for selecting best-fit models of nucleotide substitution. We specifically examine the role of the topology used to estimate the likelihood of the different models and the importance of the order in which hypotheses are tested. We do this by simulating DNA sequences under a known model of nucleotide substitution and recording how often this true model is recovered by the different methods. Our results suggest that model selection is reasonably accurate and indicate that some likelihood ratio test methods perform overall better than the Akaike or Bayesian information criteria. The tree used to estimate the likelihood scores does not influence model selection unless it is a randomly chosen tree. The order in which hypotheses are tested, and the complexity of the initial model in the sequence of tests, influence model selection in some cases. Model fitting in phylogenetics has been suggested for many years, yet many authors still arbitrarily choose their models, often using the default models implemented in standard computer programs for phylogenetic estimation. We show here that a best-fit model can be readily identified. Consequently, given the relevance of models, model fitting should be routine in any phylogenetic analysis that uses models of evolution.

Algorithms↗
PubMed1998

A genetic study of anteroposterior and vertical facial proportions using model-fitting.

Genetic model-fitting was used to determine the heritability of anteroposterior and vertical facial proportions in twins. Lateral headplates of 33 monozygotic and 46 dizygotic twins, none of whom had undergone orthodontic treatment, were used. Five proportions, based on four vertical and five horizontal measurements, were assessed: lower facial height, anterior- to posterior-facial height, total facial height to face depth, sella-A-point to sella-B-point, and sella-upper incisal edge to sella-lower incisal edge. Reproducibility was high for all variables. Model-fitting indicated that all the facial proportions were controlled by additive genes and the specific environment. The genetic component was 71% for upper-to lower-facial height, 66% for anterior- to posterior-facial height, 62% for total facial height, and 66% for sella-A-point to sella-B-point and sella-upper incisal edge to sella-lower incisal edge.

Adolescent↗
PubMed2006

Probe-level linear model fitting and mixture modeling results in high accuracy detection of differential gene expression.

BACKGROUND: The identification of differentially expressed genes (DEGs) from Affymetrix GeneChips arrays is currently done by first computing expression levels from the low-level probe intensities, then deriving significance by comparing these expression levels between conditions. The proposed PL-LM (Probe-Level Linear Model) method implements a linear model applied on the probe-level data to directly estimate the treatment effect. A finite mixture of Gaussian components is then used to identify DEGs using the coefficients estimated by the linear model. This approach can readily be applied to experimental design with or without replication. RESULTS: On a wholly defined dataset, the PL-LM method was able to identify 75% of the differentially expressed genes within 10% of false positives. This accuracy was achieved both using the three replicates per conditions available in the dataset and using only one replicate per condition. CONCLUSION: The method achieves, on this dataset, a higher accuracy than the best set of tools identified by the authors of the dataset, and does so using only one replicate per condition.

Algorithms↗
PubMed2000

Ethanol pharmacokinetics in white women: nonlinear model fitting versus zero-order elimination analyses.

BACKGROUND: Studies have shown repeatedly that ethanol pharmacokinetics are not linear, yet most researchers still determine ethanol elimination by linear, zero-order kinetics. The goals of the present work were to: (1) fit four nonlinear pharmacokinetic models to mean breath alcohol concentration (BrAC)-time data of 27 women and determine the best-fit model; (2) fit the determined best-fit model to individual BrAC data and estimate the pharmacokinetic parameters; and (3) compare the method of nonlinear model fitting with the classical zero-order elimination method and determine in which cases the classical approach is justified. METHODS: Twenty-seven healthy white women ingested four drinks (total of 0.67 g x kg(-1)) of ethanol on two test days. Approximately 24 breath ethanol samples (for pharmacokinetic analyses) and one blood sample (for hormonal markers) were taken per day. Pharmacokinetic model evaluation was based on the coefficient of variation, the weighted residual sum of squares, and the sequence of the weighted residuals. Because hormonal changes across the menstrual cycle did not significantly influence ethanol pharmacokinetics, data from the two test days were pooled. RESULTS: The best-fit model was a one-compartment open model with first-order absorption and sequential first-order elimination, followed by Michaelis-Menten elimination kinetics. Fitting this model to the individual BrAC data yielded mean ka = 0.062 hr(-1), Vd = 0.457 L x kg(-1), ke = 0.011 hr(-1), Vmax = 0.136 g x L(-1) x hr(-1), and Km = 0.096 g x L(-1). For the classical analyses, mean time to peak BrAC = 1.83 hr, disappearance rate = 0.179 g x L(-1) x hr(-1), and area under the blood ethanol-time curve (AUC) = 2.884 g x L(-1) x hr. Correlational analyses showed that more frequent drinkers eliminated ethanol significantly faster and reached significantly lower AUC than less frequent drinkers. CONCLUSIONS: After multiple dose ingestion in white women, classical zero-order elimination analyses can be applied only to a limited portion of the descending BrAC-time curve. They seem justified and practical from 0.5 hr after peak BrAC until BrAC reaches 0.2 g x L(-1). To describe ethanol pharmacokinetics across the entire BrAC-time curve, however, sophisticated nonlinear model fitting is required.

Adult↗
PubMed2005

Risks of drawing inferences about cognitive processes from model fits to individual versus average performance.

With the goal of drawing inferences about underlying processes from fits of theoretical models to cognitive data, we examined the tradeoff of risks of depending on model fits to individual performance versus risks of depending on fits to averaged data with respect to estimation of values of a model's parameters. Comparisons based on several models applied to experiments on recognition and categorization and to artificial, computer-generated data showed that results of using the two types of model fitting are strongly determined by two factors: model complexity and number of subjects. Reasonably accurate information about true parameter values was found only for model fits to individual performance and then only for some of the parameters of a complex model. Suggested guidelines are given for circumventing a variety of obstacles to successful recovery of useful estimates of a model's parameters from applications to cognitive data.

Cognition↗
PubMed2005

An application of model-fitting procedures for marginal structural models.

Marginal structural models (MSMs) are being used more frequently to obtain causal effect estimates in observational studies. Although the principal estimator of MSM coefficients has been the inverse probability of treatment weight (IPTW) estimator, there are few published examples that illustrate how to apply IPTW or discuss the impact of model selection on effect estimates. The authors applied IPTW estimation of an MSM to observational data from the Fresno Asthmatic Children's Environment Study (2000-2002) to evaluate the effect of asthma rescue medication use on pulmonary function and compared their results with those obtained through traditional regression methods. Akaike's Information Criterion and cross-validation methods were used to fit the MSM. In this paper, the influence of model selection and evaluation of key assumptions such as the experimental treatment assignment assumption are discussed in detail. Traditional analyses suggested that medication use was not associated with an improvement in pulmonary function--a finding that is counterintuitive and probably due to confounding by symptoms and asthma severity. The final MSM estimated that medication use was causally related to a 7% improvement in pulmonary function. The authors present examples that should encourage investigators who use IPTW estimation to undertake and discuss the impact of model-fitting procedures to justify the choice of the final weights.

Air Pollutants↗
PubMed2003

A model-fitting implementation of the DeFries-Fulker model for selected twin data.

In this research note, DeFries-Fulker (DF) regression analysis is reframed in model-fitting terms, where an individual's expected score is modeled as a function of their co-twin's proband status. This more flexible implementation of the DF model allows DZ-O twins to be incorporated in a sex-limitation model. Brief simulation results are presented along with the Mx scripts used.

Computer Simulation↗
PubMed2000

Modeling evolution at the protein level using an adjustable amino acid fitness model.

An adjustable fitness model for amino acid site substitutions is investigated. This model, a generalization of previously developed evolutionary models, has several distinguishing characteristics: it separately accounts for the processes of mutation and substitution, allows for heterogeneity among substitution rates and among evolutionary constraints, and does not make any prior assumptions about which sites or characteristics of proteins are important to molecular evolution. While the model has fewer adjustable parameters than the general reversible mtREV model, when optimized it outperforms mtREV in likelihood analysis on protein-coding mitochondrial genes. In addition, the optimized fitness parameters of the model show correspondence to some biophysical characteristics of amino acids.

Amino Acid Substitution↗
PubMed1991

Model fitting and projection of the AIDS epidemic.

Previously it was possible to fit detailed models to incidence data (for example, of AIDS) only by trial and error and good judgment; the large number of parameters obstructed optimization of, for example, the (approximate) likelihood. Here, we analyze a model for the spread of AIDS in a homosexual population and identify a minimal set of primary components that dictate the dynamics of the Model: the initial growth rate theta, the basic reproductive ratio R0, and the heterogeneity coefficient S. It is then shown that it is sufficient to maximize the likelihood over these three primary components; further maximization over the remaining secondary parameters does not produce a significant improvement in the fit or affect the projection of the epidemic. This method also allows construction of confidence limits for the projected incidence curve, allowing us to quantify the uncertainties associated with such model fitting procedures. The method is tested on simulation data to analyze how the accuracy of estimates and projections changes as we gain more data.

Acquired Immunodeficiency Syndrome↗
PubMedDate not supplied

Assessing model fit by cross-validation.

When QSAR models are fitted, it is important to validate any fitted model-to check that it is plausible that its predictions will carry over to fresh data not used in the model fitting exercise. There are two standard ways of doing this-using a separate hold-out test sample and the computationally much more burdensome leave-one-out cross-validation in which the entire pool of available compounds is used both to fit the model and to assess its validity. We show by theoretical argument and empiric study of a large QSAR data set that when the available sample size is small-in the dozens or scores rather than the hundreds, holding a portion of it back for testing is wasteful, and that it is much better to use cross-validation, but ensure that this is done properly.

Journal Article↗
PubMed2003

Model fitting in (n+1) dimensions.

Conventionally, fitting a mathematical model to empirically derived data is achieved by varying model parameters to minimize the deviations between expected and observed values in the dependent dimension. However, when functions to be fit are multivalued (e.g., an ellipse), conventional model fitting procedures fail. A novel (n+1)-dimensional [(n+1)-D] model fitting procedure is presented which can solve such problems by transforming the n-D model and data into (n+1)-D space and then minimizing deviations in the constructed dimension. While the (n+1)-D procedure provides model fits identical to those obtained with conventional methods for single-valued functions, it also extends parameter estimation to multivalued functions.

Algorithms↗
PubMed2004

The validity of the Neale and Kendler model-fitting approach in examining the etiology of comorbidity.

Given that knowledge regarding the etiology of comorbidity between disorders can have a significant impact on research regarding the classification, treatment, and etiology of the disorders, the ability to reject incorrect hypotheses regarding the causes of comorbidity is very important. A simulation study was conducted to assess the validity of the Neale and Kendler (1995) model-fitting approach in examining the etiology of comorbidity between two disorders. First, data were simulated under the assumptions of the 13 alternative comorbidity models described by Neale and Kendler. Second, model-fitting analyses testing the comorbidity models were conducted on the simulated datasets. Thirteen sets of data with varying model parameters were simulated to test Neale and Kendler's assertion that their model-fitting approach is appropriate across a range of potential prevalences and degrees of familiality. The validity of the model-fitting approach in examining unselected twin data and a combination of selected family data and unselected family data was explored. The model-fitting approach successfully discriminated several classes of comorbidity models, although discrimination between models within classes of related models was less accurate. Results suggest that the model-fitting approach can be a useful tool in examining the etiology of the comorbidity between disorders if the caveats of the present study's results are considered carefully. As predicted by Neale and Kendler, variations in the disorder prevalences and familial correlations did not affect the validity of their model-fitting approach, but affected the power to discriminate the correct model. As suggested by Neale and Kendler, the model-fitting approach can be applied to both unselected and selected data and to both twin and family data.

Comorbidity↗
PubMed2001

Minimizing model fitting objectives that contain spurious local minima by bootstrap restarting.

Objective functions that arise when fitting nonlinear models often contain local minima that are of little significance except for their propensity to trap minimization algorithms. The standard methods for attempting to deal with this problem treat the objective function as fixed and employ stochastic minimization approaches in the hope of randomly jumping out of local minima. This article suggests a simple trick for performing such minimizations that can be employed in conjunction with most conventional nonstochastic fitting methods. The trick is to stochastically perturb the objective function by bootstrapping the data to be fit. Each bootstrap objective shares the large-scale structure of the original objective but has different small-scale structure. Minimizations of bootstrap objective functions are alternated with minimizations of the original objective function starting from the parameter values with which minimization of the previous bootstrap objective terminated. An example is presented, fitting a nonlinear population dynamic model to population dynamic data and including a comparison of the suggested method with simulated annealing. Convergence diagnostics are discussed.

Algorithms↗