Mixed-Methods Study of Disability Self-Management in Mexican Americans With Osteoarthritis.

BACKGROUND: Health disparities in osteoarthritis (OA) outcomes exist both in the occurrence and treatment of functional limitation and disability for Mexican Americans. Although the effect of self-management of chronic illness is well established, studies demonstrate little attention to self-management of function or disability, despite the strong potential effect on both and, consequently, on patients' lives. OBJECTIVE: The purpose of this study pilot was to develop and test key variable relationships for a measure of disability self-management among Mexican Americans. METHODS: In this sequential, two-phased, mixed-methods, biobehavioral pilot study of Mexican American women and men with OA, a culturally tailored measure of disability self-management was created, and initial relationships among key variables were explored. RESULTS: First, a qualitative study of 19 adults of Mexican American descent born in Texas (United States) or Mexico was conducted. The Mexican American Disability Self-Management Scale was created using a descriptive content analysis of interview data. The scale was tested and refined, resulting in 18 items and a descriptive frequency of therapeutic management efforts. Second, correlations between study variables were estimated: Disability and function were negatively correlated. Disability correlated positively with social support and activity effort. Disability correlated negatively with disability self-management, pain, and C-reactive protein. Function was positively correlated with age, pain, and depression. Liver enzymes (alanine transaminase) correlated positively with pain and anxiety. DISCUSSION: This mixed-methods study indicates directions for further testing and interventions for disability outcomes among Mexican Americans.

First-interview response patterns of intensive longitudinal psychological and health data.

Self-report data are essential in health psychology research where an individual's perception is critical to understanding one's health and psychological status. Intensive data collection over time, including daily diary assessments, is necessary in understanding within- and between-person variability in health and psychological processes over time. An "initial elevation or latent decline" (IELD) effect, inherent of self-report data, is increasingly acknowledged in the social psychology literature, but awareness of this effect in health psychology research is lacking, particularly in studies that emphasize within- and between-person variability in self-reports. The IELD effect is a pattern in which responses tend to be more extreme at the initial interview relative to subsequent responses. This paper illustrates the impact of IELD in applications of mixed-effects models based on observational self-reports and concludes that researchers take such effects into account in data analysis or in the research designing phase to help mitigate such effects.

Alternative covariance structures in mixed-effects models: Addressing intra- and inter-individual heterogeneity.

Mixed-effects models for repeated measures and longitudinal data include random coefficients that are unique to the individual, and thus permit subject-specific growth trajectories, as well as direct study of how the coefficients of a growth function vary as a function of covariates. Although applications of these models often assume homogeneity of the within-subject residual variance that characterizes within-person variation after accounting for systematic change and the variances of the random coefficients of a growth model that quantify individual differences in aspects of change, alternative covariance structures can be considered. These include allowing for serial correlations between the within-subject residuals to account for dependencies in data that remain after fitting a particular growth model or specifying the within-subject residual variance to be a function of covariates or a random subject effect to address between-subject heterogeneity due to unmeasured influences. Further, the variances of the random coefficients can be functions of covariates to relax the assumption that these variances are constant across subjects and to allow for the study of determinants of these sources of variation. In this paper, we consider combinations of these structures that permit flexibility in how mixed-effects models are specified to understand within- and between-subject variation in repeated measures and longitudinal data. Data from three learning studies are analyzed using these different specifications of mixed-effects models.

Bayesian pattern-mixture models for dropout and intermittently missing data in longitudinal data analysis.

Valid inference can be drawn from a random-effects model for repeated measures that are incomplete if whether the data are missing or not, known as missingness, is independent of the missing data. Data that are missing completely at random or missing at random are two data types for which missingness is ignorable. Given ignorable missingness, statistical inference can proceed without addressing the source of the missing data in the model. If the missingness is not ignorable, however, recommendations are to fit multiple models that represent different plausible explanations of the missing data. A popular choice in methods for evaluating nonignorable missingness is a random-effects pattern-mixture model that extends a random-effects model to include one or more between-subjects variables that represent fixed patterns of missing data. Generally straightforward to implement, a fixed pattern-mixture model is one among several options for assessing nonignorable missingness, and when it is used as the sole model to address nonignorable missingness, understanding the impact of missingness is greatly limited. This paper considers alternatives to a fixed pattern-mixture model for nonignorable missingness that are generally straightforward to fit and encourage researchers to give greater attention to the possible impact of nonignorable missingness in longitudinal data analysis. Patterns of both monotonic and non-monotonic (intermittently) missing data are addressed. Empirical longitudinal psychiatric data are used to illustrate the models. A small Monte Carlo data simulation study is presented to help illustrate the utility of such methods.

A latent variable mixed-effects location scale model that also considers between-person differences in the autocorrelation.

In public health research an increasing number of studies is conducted in which intensive longitudinal data is collected in an experience sampling or a daily diary design. Typically, the resulting data is analyzed with a mixed-effects model or mixed-effects location scale model because they allow one to examine a host of interesting longitudinal research questions. Here, we introduce an extension of the mixed-effects location scale model in which measurement error of the observed variables is considered by a latent factor model and in which-in addition to the mean-or location-related effects-the residual variance of the latent factor and the parameters of the autoregressive process of this latent factor can differ between persons. We show how to estimate the parameters of the model with a maximum likelihood approach, whose performance is also compared with a Bayesian approach in a small simulation study. We illustrate the models using a real data example and end with a discussion in which we suggest questions for future research.

Longitudinal Effects of Sex, Aging, and Multiple Sclerosis Diagnosis on Function.

BACKGROUND: A gap in research about the trajectories of function among men and women aging with functional limitations because of multiple sclerosis (MS) hinders ability to plan for future needs. OBJECTIVES: Using a biopsychosocial model, we characterize how men and women with MS report changes over time in their function and test how person-level differences in age, diagnosis duration, and sex influence perceived function. METHODS: A longitudinal study with multiple waves of surveys was used to collect data on participant perceptions of function, as well as demographic and contextual variables. Self-reported functional limitation was measured over a decade. The study participants were community residing with physician-diagnosed MS. RESULTS: The people with MS had a diagnosis duration of about 13 years and were around 51 years of age, on average, at the start of the study. They were primarily women and non-Hispanic White. We analyzed the data using mixed-effects models. Subject-specific, functional limitation trajectories were described best with a quadratic growth model. Relative to men, women reported lower functional limitation and greater between-person variation and rates of acceleration in functional limitation scores. DISCUSSION: Results suggest function progressed through two pathways for over a decade, particularly closer to diagnoses. Variability in trajectories between individuals based on sex and years since diagnosis of disease indicates that men and women with MS may experience perceptions of their function with age differently. This has implications for clinician advice to men and women with MS.

A Latent Variable Mixed-Effects Location Scale Model with an Application to Daily Diary Data.

A mixed-effects location scale model allows researchers to study within- and between-person variation in repeated measures. Key components of the model include separate variance models to study predictors of the within-person variance, as well as predictors of the between-person variance of a random effect, such as a random intercept. In this paper, a latent variable mixed-effects location scale model is developed that combines a longitudinal common factor model and a mixed-effects location scale model to characterize within- and between-person variation in a common factor. The model is illustrated using daily reports of positive affect and daily stressors for a large sample of adult women.

Music Compared with Auditory Books: A Randomized Controlled Study Among Long-Term Care Residents with Alzheimer's Disease or Related Dementia.

BACKGROUND: Over 5 million Americans age 65 years and older were diagnosed with Alzheimer's disease and/or related dementia (ADRD), a majority of whom exhibit behavioral and psychological symptoms leading to placement in long-term care settings. These facilities need nonmedical interventions, and music-based programs have received supportive evidence. SETTING: Thirteen long-term care facilities were among a wave of facilities that volunteered to be trained and to administer a music-based intervention. The residents within were randomized into intervention or control groups (intervention/music, n = 103; control/audiobook, n = 55). DESIGN: This team used a pragmatic trial to randomly embed music and control (audiobooks) into 13 long-term care facilities to compare the effects on agitation in people with ADRD. METHODS: Measures included a demographic survey; the Mini-Mental Status Examination, used to assess cognitive status; and the Cohen-Mansfield Agitation Inventory with 4 subscales, used to measure agitation. These measures were implemented at baseline and every 2 weeks for 8 weeks. Mixed-effects models were used to evaluate change in agitation measures while addressing dependencies of scores within participants and facility. RESULTS: Decreases in agitation were attributable to both music and audiobooks in 3 of 4 agitation subscales. In the fourth, physical agitation, which was not directed toward staff, initially, it decreased given music, and increased thereafter; and generally, it increased with the audiobooks. CONCLUSION AND IMPLICATIONS: Both music and control audiobooks delivered by headphones after personalized selection reduced some aspects of agitation in residents diagnosed with ADRD. The effects of music were greater initially then diminished.

Piecewise latent growth models: beyond modeling linear-linear processes.

Piecewise latent growth models (LGMs) for linear-linear processes have been well-documented and studied in recent years. However, in the latent growth modeling literature, advancements to other functional forms as well as to multiple changepoints or knots have been nearly non-existent. This manuscript deals with three extensions. The first is to a piecewise latent growth model incorporating higher-order polynomials. The second is to extend the basic framework to three phases. The last extension is to inherently nonlinear functions. In these extensions, the changepoint(s) is a parameter to be estimated and may be fixed or allowed to vary across subjects as an application warrants. The approaches are developed and two illustrative empirical examples from psychology are used to highlight the methodological nuances. Annotated statistical software is provided to make these elaborations accessible to practitioners and methodologists.

Health psychology in the time of COVID-19.

Health Psychology has received numerous papers over the past several months on topics related to the COVID-19 pandemic. Many of them concern depression, anxiety, stress, or other forms of distress in the general population or in health care workers. We have received far fewer papers on COVID-related health behaviors and health communications-factors that have played central roles in the spread of the pandemic and that are major topics in health psychology. Our experience is consistent with the published scientific literature on the pandemic. A Medline search that we conducted in late September yielded over 23,000 English-language articles pertaining to COVID-19. Over 1,400 of them concerned topics that are within the scope of Health Psychology. As shown in Table 1, COVID-related mental disorders comprised the largest category. Many other studies concerned other forms of stress or emotional distress. At least 248 articles addressed the profound ethnic and racial disparities in COVID-19 infection and death rates and in access to health care that are accentuating longstanding health inequities; 22 (9%) of these articles addressed behavioral or psychosocial aspects of COVID-19 health disparities. Thus, the literature on the behavioral and psychosocial aspects of the pandemic has been dominated, so far at least, by research on stress or distress. Fewer reports have been published so far on critical COVID-related health behaviors, health communication, or health disparities. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

A new look at neurobehavioral development in rhesus monkey neonates (Macaca mulatta).

The Brazelton Neonatal Behavioral Assessment Scale (NBAS) evaluates a newborn infant's autonomic, motor, state, temperament, and social-attentional systems, which can help to identify infants at risk of developmental problems. Given the prevalence of rhesus monkeys being used as an animal model for human development, here we aimed to validate a standardized test battery modeled after the NBAS for use with nonhuman primates called the Infant Behavioral Assessment Scale (IBAS), employing exploratory structural equation modeling using a large sample of rhesus macaque neonates (n = 1,056). Furthermore, we examined the repeated assessments of the common factors within the same infants to describe any changes in performance over time, taking into account two independent variables (infant sex and rearing condition) that can potentially affect developmental outcomes. Results revealed three factors (Orientation, State Control, and Motor Activity) that all increased over the 1st month of life. While infant sex did not have an effect on any factor, nursery-rearing led to higher scores on Orientation but lower scores on State Control and Motor Activity. These results validate the IBAS as a reliable and valuable research tool for use with rhesus macaque infants and suggest that differences in rearing conditions can affect developmental trajectories and potentially pre-expose infants to heightened levels of cognitive and emotional deficiencies.

Two-part mixed-effects location scale models.

Longitudinal time use data afford the opportunity to study within- and between-individual differences, but can present challenges in data analysis. Often the response set includes a large number of zeros representing those who did not engage in the target behavior. Coupled with this is a continuous measure of time use for those who did engage. The latter is strictly positive and skewed to the right if relatively few individuals engage in the behavior to a greater extent. Data analysis is further complicated for repeated measures, because within-individual responses are typically correlated, and some respondents may have missing data. This combination of zeros and positive responses is characteristic of a type of semicontinuous data in which the response is equal to a discrete value and is otherwise continuous. Two-part models have been successfully applied to cross-sectional time use data when the research goals distinguish between a respondent's likelihood to engage in a behavior and the time spent conditional on any time being spent, as these models allow different covariates to relate to each distinct aspect of a behavior. Two-part mixed-effects models extend two-part models for analysis of longitudinal semicontinuous data to simultaneously address longitudinal decisions to engage in a behavior and time spent conditional on any time spent. Heterogeneity between and within individuals can be studied in unique ways. This paper presents applications of these models to daily diary data to study individual differences in time spent relaxing or engaged in leisure activities for an adult sample.

A Capabilities Approach to Environmental Impact on Nursing Home Resident Quality of Life.

Nursing homes are the major provider of intermediate and long-term care outside of the hospital setting to individuals whose capacity for self-care is limited due to physical or cognitive impairments. Yet, despite their need for assistance, residents of nursing homes want to control their lives, set their routines, and do enjoyable things. The extent to which residents can maintain autonomy and dignity is important. The current study suggests an environmental gerontological framework, rooted in a capabilities approach, that can be used to consider environmental impact on quality of life in nursing homes. Using a cross-sectional survey of nursing home residents in Texas, environmental factors that might predict residents' quality of life as well as possible interactions of environmental factors and residents' characteristics that might predict well-being were examined. Environmental orientation and perception of social activities were important predictors of residents' quality of life, but geographic location and facility size were not important predictors. [Res Gerontol Nurs. 2017; 10(4):162-170.].

Do "birds of a feather flock together" or do "opposites attract"? Behavioral responses and temperament predict success in pairings of rhesus monkeys in a laboratory setting.

The growing recognition that social needs of primates in captivity must be addressed can present challenges to staff at primate facilities charged with implementing pair-housing solutions for animals. Unfortunately, there are few published papers that identify individual characteristics that might facilitate the social pairing process, and those that have looked at pre-pairing measures of behavior have produced mixed results. Using a database of n = 340 isosexual pairing attempts, we report that measures associated with responses to a standardized infant assessment protocol (the BioBehavioral Assessment program) predict success in pairing attempts that occurred years later. Behavioral responses to a brief separation and relocation, to a human intruder challenge, as well as ratings of temperament, were obtained from rhesus monkeys at 3-4 months of age. Logistic regression was used to identify potential predictors of success when animals were paired up to 10 years after the behavioral assessments. Among females, success was higher when members of a pair were more similar (i.e., a smaller difference scores) in patterns of emotional responding (Emotionality, Nervous temperament) during the infant assessments. In contrast, among males, success was higher when the pair had lower mean values for Gentle and Nervous temperament scores; when the members were younger; when pairs had a greater weight difference; and when they came from the same rearing background. Together, our results suggest that broad measures reflecting patterns of emotionality in response to challenge, which can be assessed in infancy (but which remain relatively stable throughout life) can be usefully employed to increase the likelihood of success in pairing attempts. Am. J. Primatol. 79:e22464, 2017. © 2015 Wiley Periodicals, Inc.

Cognitive reappraisal and expressive suppression: Links to racial-ethnic discrimination and adjustment among Latino/a and Asian-heritage college students.

OBJECTIVE: We examined whether two key emotion regulation strategies, cognitive reappraisal and expressive suppression, moderated the relations between discrimination (i.e., foreigner objectification and general denigration) and adjustment. METHODS: Participants were U.S. Latino/a and Asian-heritage college students (N = 1,279, 67% female, 72% U.S. born) from the Multi-Site University Study of Identity and Culture (MUSIC). Students completed online self-report surveys in 2009. RESULTS: Multi-group path analysis demonstrated that a fully constrained model fit well for both Latino/a and Asian-heritage student data. The results showed that with increasing levels of denigration (but not foreigner objectification), the combination of lower cognitive reappraisal and higher expressive suppression was related to greater depressive symptoms, anxiety, and aggression. CONCLUSIONS: Our findings highlight the importance of examining multiple emotion regulation strategies simultaneously-considering what strategies are available to individuals and in what combination they are used-to understand how best to deal with negative emotions resulting from experiencing discrimination.

A Note on Recurring Misconceptions When Fitting Nonlinear Mixed Models.

Nonlinear mixed-effects (NLME) models are used when analyzing continuous repeated measures data taken on each of a number of individuals where the focus is on characteristics of complex, nonlinear individual change. Challenges with fitting NLME models and interpreting analytic results have been well documented in the statistical literature. However, parameter estimates as well as fitted functions from NLME analyses in recent articles have been misinterpreted, suggesting the need for clarification of these issues before these misconceptions become fact. These misconceptions arise from the choice of popular estimation algorithms, namely, the first-order linearization method (FO) and Gaussian-Hermite quadrature (GHQ) methods, and how these choices necessarily lead to population-average (PA) or subject-specific (SS) interpretations of model parameters, respectively. These estimation approaches also affect the fitted function for the typical individual, the lack-of-fit of individuals' predicted trajectories, and vice versa.

Exploitation of Interleukin-10 (IL-10) Signaling Pathways: Alternate Roles of Viral and Cellular IL-10 in Rhesus Cytomegalovirus Infection.

There is accumulating evidence that the viral interleukin-10 (vIL-10) ortholog of both human and rhesus cytomegalovirus (HCMV and RhCMV, respectively) suppresses the functionality of cell types that are critical to contain virus dissemination and help shape long-term immunity during the earliest virus-host interactions. In particular, exposure of macrophages, peripheral blood mononuclear cells, monocyte-derived dendritic cells, and plasmacytoid dendritic cells to vIL-10 suppresses multiple effector functions including, notably, those that link innate and adaptive immune responses. Further, vaccination of RhCMV-uninfected rhesus macaques with nonfunctional forms of RhCMV vIL-10 greatly restricted parameters of RhCMV infection following RhCMV challenge of the vaccinees. Vaccinees exhibited significantly reduced shedding of RhCMV in saliva and urine following RhCMV challenge compared to shedding in unvaccinated controls. Based on the evidence that vIL-10 is critical during acute infection, the role of vIL-10 during persistent infection was analyzed in rhesus macaques infected long term with RhCMV to determine whether postinfection vaccination against vIL-10 could change the virus-host balance. RhCMV-seropositive macaques, which shed RhCMV in saliva, were vaccinated with nonfunctional RhCMV vIL-10, and shedding levels of RhCMV in saliva were evaluated. Following robust increases in vIL-10-binding and vIL-10-neutralizing antibodies, shedding levels of RhCMV modestly declined, consistent with the interpretation that vIL-10 may play a functional role during persistent infection. However, a more significant association was observed between the levels of cellular IL-10 secreted in peripheral blood mononuclear cells exposed to RhCMV antigens and shedding of RhCMV in saliva. This result implies that RhCMV persistence is associated with the induction of cellular IL-10 receptor-mediated signaling pathways. IMPORTANCE: Human health is adversely impacted by viruses that establish lifelong infections that are often accompanied with increased morbidity and mortality (e.g., infections with HIV, hepatitis C virus, or human cytomegalovirus). A longstanding but unfulfilled goal has been to develop postinfection vaccine strategies that could "reboot" the immune system of an infected individual in ways that would enable the infected host to develop immune responses that clear reservoirs of persistent virus infection, effectively curing the host of infection. This concept was evaluated in rhesus macaques infected long term with rhesus cytomegalovirus by repeatedly immunizing infected animals with nonfunctional versions of the rhesus cytomegalovirus-encoded viral interleukin-10 immune-modulating protein. Following vaccine-mediated boosting of antibody titers to viral interleukin-10, there was modest evidence for increased immunological control of the virus following vaccination. More significantly, data were also obtained that indicated that rhesus cytomegalovirus is able to persist due to upregulation of the cellular interleukin-10 signaling pathway.

Overcoming Clinical Inertia: A Randomized Clinical Trial of a Telehealth Remote Monitoring Intervention Using Paired Glucose Testing in Adults With Type 2 Diabetes.

BACKGROUND: Type 2 diabetes mellitus is a worldwide challenge. Practice guidelines promote structured self-monitoring of blood glucose (SMBG) for informing health care providers about glycemic control and providing patient feedback to increase knowledge, self-efficacy, and behavior change. Paired glucose testing­pairs of glucose results obtained before and after a meal or physical activity­is a method of structured SMBG. However, frequent access to glucose data to interpret values and recommend actions is challenging. A complete feedback loop­data collection and interpretation combined with feedback to modify treatment­has been associated with improved outcomes, yet there remains limited integration of SMBG feedback in diabetes management. Incorporating telehealth remote monitoring and asynchronous electronic health record (EHR) feedback from certified diabetes educators (CDEs)­specialists in glucose pattern management­employ the complete feedback loop to improve outcomes. OBJECTIVE: The purpose of this study was to evaluate a telehealth remote monitoring intervention using paired glucose testing and asynchronous data analysis in adults with type 2 diabetes. The primary aim was change in glycated hemoglobin (A(1c))­a measure of overall glucose management­between groups after 6 months. The secondary aims were change in self-reported Summary of Diabetes Self-Care Activities (SDSCA), Diabetes Empowerment Scale, and Diabetes Knowledge Test. METHODS: A 2-group randomized clinical trial was conducted comparing usual care to telehealth remote monitoring with paired glucose testing and asynchronous virtual visits. Participants were aged 30-70 years, not using insulin with A1c levels between 7.5% and 10.9% (58-96 mmol/mol). The telehealth remote monitoring tablet computer transmitted glucose data and facilitated a complete feedback loop to educate participants, analyze actionable glucose data, and provide feedback. Data from paired glucose testing were analyzed asynchronously using computer-assisted pattern analysis and were shared with patients via the EHR weekly. CDEs called participants monthly to discuss paired glucose testing trends and treatment changes. Separate mixed-effects models were used to analyze data. RESULTS: Participants (N=90) were primarily white (64%, 56/87), mean age 58 (SD 11) years, mean body mass index 34.1 (SD 6.7) kg/m2, with diabetes for mean 8.2 (SD 5.4) years, and a mean A(1c) of 8.3% (SD 1.1; 67 mmol/mol). Both groups lowered A(1c) with an estimated average decrease of 0.70 percentage points in usual care group and 1.11 percentage points in the treatment group with a significant difference of 0.41 percentage points at 6 months (SE 0.08, t159=-2.87, P=.005). Change in medication (SE 0.21, t157=-3.37, P=.009) was significantly associated with lower A(1c) level. The treatment group significantly improved on the SDSCA subscales carbohydrate spacing (P=.04), monitoring glucose (P=.001), and foot care (P=.02). CONCLUSIONS: An eHealth model incorporating a complete feedback loop with telehealth remote monitoring and paired glucose testing with asynchronous data analysis significantly improved A(1c) levels compared to usual care. TRIAL REGISTRATION: Clinicaltrials.gov NCT01715649; https://www.clinicaltrials.gov/ct2/show/NCT01715649 (Archived by WebCite at http://www.webcitation.org/6ZinLl8D0).

The timing of entry into adult roles and changes in trajectories of problem behaviors during the transition to adulthood.

This study of a cohort of 451 adolescents examined associations between trajectories of problem behaviors and the timing of entry into work, marriage, and parenthood. We used data from 12 assessments across adolescence, through emerging adulthood and into young adulthood. We employed 2-phase mixed-effects models to estimate growth in substance use and antisocial behavior across adolescence, deceleration in the period that follows, and the change point that marks the transition between the 2 phases. We then examined the degree to which the timing of entry into a specific adult role was associated with change in problem behaviors and the change point between the 2 phases. We hypothesized that earlier entries into adult roles would be associated with earlier transitions to the decline in problem behaviors generally observed during adulthood but that later entries would be associated with more quickly declining rates of problem behaviors during adulthood. As proposed, earlier entries into marriage and parenthood predicted earlier transitions to declining trajectories in both substance use and antisocial behavior during adulthood. The findings also indicated that delayed marriage and parenthood were associated with more quickly decreasing rates of change in substance use, but not antisocial behavior, during adulthood. Thus, the results are consistent with the idea that substance use decreases earlier but not as quickly during adulthood for those with earlier entries into marriage and parenthood. However, the timing of entry into work did not predict trajectory changes. (PsycINFO Database Record (c) 2014 APA, all rights reserved).

On Fitting a Multivariate Two-Part Latent Growth Model.

A 2-part latent growth model can be used to analyze semicontinuous data to simultaneously study change in the probability that an individual engages in a behavior, and if engaged, change in the behavior. This article uses a Monte Carlo (MC) integration algorithm to study the interrelationships between the growth factors of 2 variables measured longitudinally where each variable can follow a 2-part latent growth model. A SAS macro implementing Mplus is developed to estimate the model to take into account the sampling uncertainty of this simulation-based computational approach. A sample of time-use data is used to show how maximum likelihood estimates can be obtained using a rectangular numerical integration method and an MC integration method.