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PubMed1979

The use of linear models and matrix least squares in clinical chemistry.

We present a unified approach to the use of linear models and matrix least squares with the intention of providing a better understanding of the techniques themselves and of the statistics that arise from these techniques as they are used in clinical chemistry. Emphasis is placed on the importance of appropriate experimental designs and adequately precise measurement processes for efficiently obtaining the desired information.

Chemistry, Clinical↗

PubMed2003

Longitudinal hierarchical linear modeling analyses of California Psychological Inventory data from age 33 to 75: an examination of stability and change in adult personality.

Twenty aspects of personality assessed via the California Psychological Inventory (CPI; Gough & Bradley, 1996) from age 33 to 75 were examined in a sample of 279 individuals. Oakland Growth Study and Berkeley Guidance Study members completed the CPI a maximum of 4 times. We used longitudinal hierarchical linear modeling (HLM) to ask the following: Which personality characteristics change and which do not? Five CPI scales showed uniform lack of change, 2 showed heterogeneous change giving an averaged lack of change, 4 showed linear increases with age, 2 showed linear decreases with age, 4 showed gender or sample differences in linear change, 1 showed a quadratic peak, and 2 showed a quadratic nadir. The utility of HLM becomes apparent in portraying the complexity of personality change and stability.

Adult↗

PubMed1996

Least squares Lehmann-Scheffé estimation of variances and covariances with mixed linear models.

Variances of quadratic estimators of (co)variances are functions of the numeric values of the (co)variance parameters being estimated. This situation makes estimation of (co)variances problematical. Uniformly best quadratic, unbiased estimators exist for balanced designs but not for unbalanced designs. This article tackles the problem by providing explicit quadratic estimators of (co)variances that are uniformly best in the sense that they are uniformly minimum variance, unbiased to the maximum extent possible over the entire range of possible parameter values of the (co)variances being estimated. This was accomplished by determining the restrictions on the elements of the matrix of the quadratic-form matrix necessary to satisfy the Lehmann-Scheffé criterion for uniformly minimum variance, unbiased estimation and then solving the resulting linear equations via the principle of least squares. The context is any mixed linear model, and the approach does not require that there be equal numbers of observations in the case of multivariate data. A detailed development of the method is given. That the procedure is completely general is discussed. A modification that forces unbiasedness is presented. An example with a three-variance-component model is provided and results discussed. A miscellaneous section discusses, among other topics, how this method can be used to compare other (co)variance component estimation procedures. The final section illustrates how the method handles multivariate situations (i.e., models with both variances and covariances) by detailing the expressions involved with the bivariate model.

Analysis of Variance↗

PubMed2003

Linear models for assessing mechanisms of sperm competition: the trouble with transformations.

Although sperm competition is a pervasive selective force shaping the reproductive tactics of males, the mechanisms underlying different patterns of sperm precedence remain obscure. Parker et al. (1990) developed a series of linear models designed to identify two of the more basic mechanisms: sperm lotteries and sperm displacement; the models can be tested experimentally by manipulating the relative numbers of sperm transferred by rival males and determining the paternity of offspring. Here we show that tests of the model derived for sperm lotteries can result in misleading inferences about the underlying mechanism of sperm precedence because the required inverse transformations may lead to a violation of fundamental assumptions of linear regression. We show that this problem can be remedied by reformulating the model using the actual numbers of offspring sired by each male, and log-transforming both sides of the resultant equation. Reassessment of data from a previous study (Sakaluk and Eggert 1996) using the corrected version of the model revealed that we should not have excluded a simple sperm lottery as a possible mechanism of sperm competition in decorated crickets, Gryllodes sigillatus.

Animals↗

PubMed1991

Adjustment for non-differential misclassification error in the generalized linear model.

It is well known that estimates of association between an outcome variable and a set of categorical covariates, some of which are measured with misclassification, tend to be biased upon application of the usual methods of estimation that ignore the classification error. We propose a method to adjust for misclassification in covariates when one applies the generalized linear model. In the case where one can observe some true covariates only through surrogates, we combine a latent class analysis with the approach to incorporate multiple surrogates into the model. We include discussion on the efficacy of repeated measurements which one can view as a special case of multiple surrogates with identical distribution. We provide two examples to demonstrate the applicability of the method and the efficacy of multiple replicates for a covariate subject to misclassification in a regression framework.

Adolescent↗

PubMed1995

Location-scale cumulative odds models for ordinal data: a generalized non-linear model approach.

Proportional odds regression models for multinomial probabilities based on ordered categories have been generalized in two somewhat different directions. Models having scale as well as location parameters for adjustment of boundaries (on an unobservable, underlying continuum) between categories have been employed in the context of ROC analysis. Partial proportional odds models, having different regression adjustments for different multinomial categories, have also been proposed. This paper considers a synthesis and further generalization of these two families. With use of a number of examples, I discuss and illustrate properties of this extended family of models. Emphasis is on the computation of maximum likelihood estimates of parameters, asymptotic standard deviations, and goodness-of-fit statistics with use of non-linear regression programs in standard statistical software such as SAS.

Humans↗

PubMedDate not supplied

Study of the relationship between organizational culture and organizational outcomes using hierarchical linear modeling methodology.

This study examines how perceptions of organizational culture influence organizational outcomes, specially, individual employee job satisfaction. The study was conducted in the health care industry in the United States. It examined the data on employee perceptions of job attributes, organizational culture, and job satisfaction, collected by Press Ganey Associates from 88 hospitals across the country in 2002-2003. Hierarchical linear modeling was used to test how organizational culture affects individual employee job satisfaction. Results indicated that some dimensions of organizational culture, specifically, job security and performance recognition, play a role in improving employee job satisfaction.

Data Collection↗

PubMed2006

The epidemiology of atypical mycobacterial diseases in northern England: a space-time clustering and Generalized Linear Modelling approach.

The incidence of infection by mycobacteria, other than tubercle bacilli (MOTT) is increasing in the United Kingdom, Europe and the United States. These diseases increase morbidity and are an increasing public health concern. However, the epidemiology of disease due to these species is not well characterized. We used space-time clustering approaches and Generalized Linear Modelling to investigate the potential predictors of disease in cases of infection by organisms of the Mycobacterium avium complex (MAC) and M. malmoense recorded in the north of England during 2000-2005. There was significant spatial and temporal clustering in juvenile cases of infection by MAC but not for cases of infection in adults by either species. There were no significant predictors of infection by M. malmoense or juvenile cases of M. avium. Incidence of disease caused by M. avium in adults was significantly related to health deprivation and weakly related to rainfall. We consider possible reasons for the difference in epidemiology in infection by M. avium in adults and juveniles.

England↗

PubMed1998

Constraints on general slowing: a meta-analysis using hierarchical linear models with random coefficients.

General slowing (GS) theories are often tested by meta-analysis that model mean latencies of older adults as a function of mean latencies of younger adults. Ordinary least squares (OLS) regression is inappropriate for this purpose because it fails to account for the nested structure of multitask response time (RT) data. Hierarchical linear models (HLM) are an alternative method for analyzing such data. OLS analysis of data from 21 studies that used iterative cognitive tasks supported GS; however, HLM analysis demonstrated significant variance in slowing across experimental tasks and a process-specific effect by showing less slowing for memory scanning than for visual-search and mental-rotation tasks. The authors conclude that HLM is more suitable than OLS methods for meta-analyses of RT data and for testing GS theories.

Aged↗

PubMed2002

Analysis of ulcer data using hierarchical generalized linear models.

In multi-centre clinical trials, heterogeneities in individual hospital treatment effects can be modelled as random effects. Estimates of the individual hospital treatment effects and estimate of the mean treatment effect, allowing for the presence of overall hospital differences, are required, together with some measure of their uncertainty. Systematic inferences from the hierarchical-likelihood are now possible, using hierarchical generalized linear models. We show how to construct profile likelihoods for the treatment effects of individual hospitals.

Data Interpretation, Statistical↗

PubMed2005

Hierarchical linear modeling analyses of the NEO-PI-R scales in the Baltimore Longitudinal Study of Aging.

The authors examined age trends in the 5 factors and 30 facets assessed by the Revised NEO Personality Inventory in Baltimore Longitudinal Study of Aging data (N=1,944; 5,027 assessments) collected between 1989 and 2004. Consistent with cross-sectional results, hierarchical linear modeling analyses showed gradual personality changes in adulthood: a decline in Neuroticism up to age 80, stability and then decline in Extraversion, decline in Openness, increase in Agreeableness, and increase in Conscientiousness up to age 70. Some facets showed different curves from the factor they define. Birth cohort effects were modest, and there were no consistent Gender x Age interactions. Significant nonnormative changes were found for all 5 factors; they were not explained by attrition but might be due to genetic factors, disease, or life experience.

Adult↗

PubMed1998

An evaluation of linear model analysis techniques for processing images of microcirculation activity.

Sequences of images of the cortical surface can be processed to reveal information about the cortical microcirculation, regional cerebral blood flow (rCBF), and changes induced by neuronal activity. This study examined the use of different analysis methodologies on intrinsic optical images taken from rat sensory motor cortex and testes. Generalized linear model (GLM) analysis was used and compared with standard signal processing methods including principal component analysis. The GLM method has been used by Friston et al. (1994, Hum. Brain Map., 1: 214-220) in the analysis of functional magnetic resonance imagery to identify regions of focal activity. We investigated the use of this method to analyze video image data of the modulation of rCBF from rat cortex. The results revealed spatiotemporal variations in rCBF in response to stimulation within local regions of cortex. The advantage of the GLM method is that it augments ordinary signal processing methods with an estimate of statistical reliability. The use of different wavelengths of illumination reveals spatial structures with different temporal relationships. In image time series data collected under green and red illumination a phase difference was found in the low frequency approximately 0.1 Hz vasomotion oscillation. This phase difference occurred in data from both cortex and testes. A possible explanation of these differences is that the spectral absorption characteristics of the tissue reflect changes in the volume proportions of the different hemoglobin derivatives in interacting with the modulation of the volume of blood. It is suggested that the combination of these effects produces the phase differences we detect.

Animals↗

PubMed2006

Linear model and algorithm to automatically estimate the pressure limit of pressure controlled ventilation for delivering a target tidal volume.

OBJECTIVE: To theoretically assess the viability of an automatic procedure to support the anesthesiologist in properly setting mechanical ventilators when the operating conditions are switched from volume controlled to pressure controlled ventilation whilst maintaining the preset tidal volume. The procedure is based on a simple linear model of the ventilator breathing system with constant parameters and utilizes the signals gathered by the ventilator without the need to add further equipment. After a short period of stable volume controlled ventilation with the desired tidal volume, the herewith described algorithm allows the calculation of the value of pressure limit to set in pressure controlled mode which assures the previously settled tidal volume with the same breathing frequency and inspiratory-expiratory time ratio. METHODS: The algorithm allows the online identification of the four parameters necessary for the mathematical model that are obtained by means of a direct comparison between the pressure, flow and volume waveforms generated by the model and the analog signals provided by the ventilator. The theoretical approach was validated by two different ventilators, various settings, two breathing circuits, endotracheal tubes of various sizes and two mechanical simulators of the respiratory system operating in various conditions. RESULTS: Errors usually less than 5% (p < 0.05) on the target tidal volume were obtained for various settings typically used for adult ventilation in less than 10 s. The theoretical approach shows its limitations (errors of 10+/- 5%, p < 0.05) at high breathing frequencies (30-40 bpm) and low tidal volumes (200-300 ml). CONCLUSIONS: The proposed theoretical approach shows the viability, for adult settings, of one of the simplest mathematical model for mechanical ventilation in order to quickly and safely switch from volume controlled to pressure controlled ventilation. The algorithm could easily be in perspective implemented in the software of the ventilator providing the anesthesiologist with an indication on the value of pressure limit to set in order to safely switch ventilation mode.

Algorithms↗

PubMed2006

Analysis of functional image analysis contest (FIAC) data with brainvoyager QX: From single-subject to cortically aligned group general linear model analysis and self-organizing group independent component analysis.

The Functional Image Analysis Contest (FIAC) 2005 dataset was analyzed using BrainVoyager QX. First, we performed a standard analysis of the functional and anatomical data that includes preprocessing, spatial normalization into Talairach space, hypothesis-driven statistics (one- and two-factorial, single-subject and group-level random effects, General Linear Model [GLM]) of the block- and event-related paradigms. Strong sentence and weak speaker group-level effects were detected in temporal and frontal regions. Following this standard analysis, we performed single-subject and group-level (Talairach-based) Independent Component Analysis (ICA) that highlights the presence of functionally connected clusters in temporal and frontal regions for sentence processing, besides revealing other networks related to auditory stimulation or to the default state of the brain. Finally, we applied a high-resolution cortical alignment method to improve the spatial correspondence across brains and re-run the random effects group GLM as well as the group-level ICA in this space. Using spatially and temporally unsmoothed data, this cortex-based analysis revealed comparable results but with a set of spatially more confined group clusters and more differential group region of interest time courses.

Algorithms↗

PubMed1994

A method for correction of CA/C ratio based on linear model of accommodation and vergence.

Measurement of the response CA/C ratio has required that the target used to stimulate the vergence system provides no blur information to the accommodative system. Although several methods have been proposed to open the accommodative feedback loop, it is difficult to ensure that a vergence target produces no stimulus for accommodation. To avoid this problem, we have derived a formula based on a linear model of the accommodative and vergence systems that allows the CA/C ratio to be estimated when the accommodative loop is not opened completely. An experiment was conducted to verify the derived formula. Two targets, Snellen letters and a small point source, were used to provide different blur-inputs to the accommodative system. CA/C ratios were estimated from the formula using measures of accommodation and vergence obtained with these two targets for eight subjects and showed a high correlation. The formula, therefore, was shown to provide a consistent estimate of the CA/C even when the accommodative loop was not opened completely.

Accommodation, Ocular↗

PubMed1999

A comparison of traditional approaches to hierarchical linear modeling when analyzing longitudinal data.

Longitudinal designs typically involve repeated time-ordered observations for each individual (or unit). Such designs are uniquely suited to studying changes over time within individuals, and relating these to individual characteristics to identify processes and causes of intra- individual changes and interindividual differences in physiologic and psychological development. The purpose of this paper is to compare and contrast univariate and multivariate ANOVA with repeated measures to hierarchical linear modeling as approaches to analyzing such longitudinal data. This will enable researchers to choose the approach that best meets their research needs, and it will enable them to compare research results that are reported using one analytical approach with results that are reported using the other approach.

Analysis of Variance↗

PubMed2000

Assessing exposure to violence using multiple informants: application of hierarchical linear model.

The present study assesses the effects of demographic risk factors on children's exposure to violence (ETV) and how these effects vary by informants. Data on exposure to violence of 9-, 12-, and 15-year-olds were collected from both child participants (N = 1880) and parents (N = 1776), as part of the assessment of the Project on Human Development in Chicago Neighborhoods (PHDCN). A two-level hierarchical linear model (HLM) with multivariate outcomes was employed to analyze information obtained from these two different groups of informants. The findings indicate that parents generally report less ETV than do their children and that associations of age, gender, and parent education with ETV are stronger in the self-reports than in the parent reports. The findings support a multivariate approach when information obtained from different sources is being integrated. The application of HLM allows an assessment of interactions between risk factors and informants and uses all available data, including data from one informant when data from the other informant is missing.

Adolescent↗

PubMed1997

Characterizing the response of PET and fMRI data using multivariate linear models.

This paper presents a new method for characterizing brain responses in both PET and fMRI data. The aim is to capture the correlations between the scans of an experiment and a set of external predictor variables that are thought to affect the scans, such as type, intensity, or shape of stimulus response. Its main feature is a Canonical Variates Analysis (CVA) of the estimated effects of the predictors from a multivariate linear model (MLM). The advantage of this over current methods is that temporal correlations can be incorporated into the model, making the MLM method suitable for fMRI as well as PET data. Moreover, tests for the presence of any correlation, and inference about the number of canonical variates needed to capture that correlation, can be based on standard multivariate statistics, rather than simulations. When applied to an fMRI data set previously analyzed by another CVA method, the MLM method reveals a pattern of responses that is closer to that detected in an earlier non-CVA analysis.

Analysis of Variance↗