Multivariate Analysis of Variance

This article examines quantitative panel analysis techniques appropriate for situations in which the researcher models determinants of change in continuous outcomes. One set of techniques, based on the analysis of pooled time-series data sets, has received little attention in the family literature, although there are a number of situations where these techniques would be appropriate, such as the analysis of multiple-wave panel data. The article explores the fixed effect (change-scare) and random effects models based on pooled time-series data and discusses their advantages and disadvantages for the analysis of survey panel data compared with other available approaches. An empirical example of these methods is presented in which the effect of marital duration and number of children on spousal interaction in intact marriages was examined in a four-wave panel sample. A significant development in the field of family research has been the increased availability of large panel survey data sets containing variables of interest to family researchers (e.g., National Survey of Families and Households Panel, Panel Study of Income Dynamics, National Longitudinal Survey of Youth, Marital Instability Over the Life Course Panel). The potential posed by these panel studies is often unrealized because of the greater complexity of panel analyses and the shortage of clear and accessible guidelines for selecting the appropriate analysis models and statistical software. Several guides to panel methods are available (e.g., Campbell, Mutran, & Parker, 1986; Collins & Horn, 1991; Finkel, 1995; Johnson, 1988; Kessler & Greenberg, 1981; Markus, 1979; Menard, 1991). While these guides can be of value, they have the following drawbacks: Some recent developments are not covered, the focus has been largely on methods for two-wave panels, and situations commonly encountered by family researchers in the analysis of survey data, such as missing waves for some respondents, have been neglected. One type of model commonly found in family research involves the analysis of change over time in a continuous dependent variable. For example, a researcher interested in explaining change in marital interaction over the course of a marriage may model the effects of increased duration of the marriage, changes in the number and ages of the children, spells of employment of both spouses, and changes in family income. This situation involves a continuous dependent variable (degree of spousal interaction) with continuous variables (marital duration, income) and events (addition and subtraction of children, spells of employment and unemployment) as explanatory variables. Panel studies of changes in psychological distress brought about by marital dissolution, changes in frequency of sexual intercourse over the duration of the marriage, and the effect of retirement on marital happiness are research problems with similar analytic needs. With two or more waves of panel data and a continuous dependent variable, the researcher has a choice among five basic panel analysis models. These are (a) regression with lagged dependent variables, (b) structural equation models with reciprocal and lagged effects (e.g., LISREL), (c) repeated measures analysis of variance, (d) growth curve and hierarchical effects models, and (e) fixed (change-score) and random effects regression estimators for pooled time-series data sets. Event history, or hazard, models (Teachman, 1982) and panel models for qualitative variables (Clogg, Eliason, & Grego, 1990) are excluded from this list because they are not designed for use with continuous dependent variables. The first three techniques have been widely used with panel data in the family literature, and are generally accessible to the researcher. Many of the regression techniques have been superseded by the structural equation approaches, which are capable of estimating reciprocal effects and control for biases introduced by measurement errors and autocorrelated errors. …

To assess the relationship between nutritional status and some factors related with poverty (acute diarrhea and overcrowding) in children less than 6 years of age in Bogotá. A community-based, cross-sectional study, was conducted during 2000 in the urban area of Bogotá, using a household interview survey. 3081 adults having in their homes children under five years were interviewed. This number of participants was calculated to obtain a representative sample of the city for estimating a binomial population parameter. A multistage sampling was carried out. The sample size was reduced to 2833 with the elimination of cases missing scores on dependent variables (DVs). Cephalic and brachial perimeters (continuous variables), used as a proxy of nutritional status (DVs), were selected as the main outcome measures. A 2 x 2 x 2 multivariate analysis of variance was performed on two DVs. Independent variables were overcrowding (as a measure of marginalization) and recent acute diarrhea. The analyses included sequential adjustment for nonorthogonality. DVs showed a low correlation (r=0.3) and a symmetric distribution. Evaluation of assumptions of linearity and multicollinearity were satisfactory. The omnibus test, using Wilk's criterion, showed that combined DVs were significantly affected by recent acute diarrhea (F=9.65 p=0.000), age less than 1 year (F=350.81 p=0.000) and the interaction acute diarrhea x overcrowding (F=6.25 p=0.000). In order to evaluate the impact of each main effect on the individual DVs, a Roy-Bargmann stepdown analysis was carried out. Homogeneity of regression was achieved for all components of the stepdown analysis. The brachial perimeter has a unique contribution to predict recent acute diarrhea (Roy-Bargmann F(1,1)=13.1 p=0.000). The cephalic perimeter has a unique contribution to predict acute diarrhea and overcrowding (Roy-Bargmann F(1,1)=10.22 p=0.001). Recent acute diarrhea and overcrowding are related with poor nutritional status. Brachial and cephalic perimeters could be attractive indicators of different varieties of nutritional deficiency.

Multivariate analysis refers to statistical techniques that simultaneously look at three or more variables in relation to the subjects under investigation with the aim of identifying or clarifying the relationships between them. These techniques have been broadly classified as dependence techniques, which explore the relationship between one or more dependent variables and their independent predictors, and interdependence techniques, that make no such distinction but treat all variables equally in a search for underlying relationships. Multiple linear regression models a situation where a single numerical dependent variable is to be predicted from multiple numerical independent variables. Logistic regression is used when the outcome variable is dichotomous in nature. The log-linear technique models count type of data and can be used to analyze cross-tabulations where more than two variables are included. Analysis of covariance is an extension of analysis of variance (ANOVA), in which an additional independent variable of interest, the covariate, is brought into the analysis. It tries to examine whether a difference persists after “controlling” for the effect of the covariate that can impact the numerical dependent variable of interest. Multivariate analysis of variance (MANOVA) is a multivariate extension of ANOVA used when multiple numerical dependent variables have to be incorporated in the analysis. Interdependence techniques are more commonly applied to psychometrics, social sciences and market research. Exploratory factor analysis and principal component analysis are related techniques that seek to extract from a larger number of metric variables, a smaller number of composite factors or components, which are linearly related to the original variables. Cluster analysis aims to identify, in a large number of cases, relatively homogeneous groups called clusters, without prior information about the groups. The calculation intensive nature of multivariate analysis has so far precluded most researchers from using these techniques routinely. The situation is now changing with wider availability, and increasing sophistication of statistical software and researchers should no longer shy away from exploring the applications of multivariate methods to real-life data sets.

Linear regression is used to describe the relationship between a continuous dependant variable of interest (outcome) and other patient characteristics or predictors (independent continuous, categorical or dichotomous variables). Fitting a linear regression model estimates a constant, predictor coefficients and their corresponding 95% confidence intervals (95%CI). In a univariable analysis only one independent variable is included in the model and the model shows the association between that variable and the outcome, without any consideration of other characteristics. In a multivariable analysis more than one predictor is included in the model.

Simultaneous estimation of discrete outcome and continuous dependent variable equations: A bivariate random effects modeling approach with unrestricted instruments

Age and Frailty Influence Hip and Knee Arthroplasty Reimbursement in a Bundled Payment Care Improvement Initiative

Morphometrics is a quantitative analysis depending on the shape and size of several specimens. Morphometric quantitative analyses are commonly used to analyse fossil record, shape and size of specimens and others. The aim of the study is to find the differences between rocky mountain wolves and arctic wolves based on gender. The sample utilised secondary data which included seven variables as independent variables and two dependent variables. Statistical modelling was used in the analysis such was the analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA). The results showed there exist differentiating results between arctic wolves and rocky mountain wolves based on independent factors and gender.

For people living with HIV/AIDS (PLWHA) positive social support networks (SSNs) can help improve quality of life, overall well-being, coping, and decrease mood disturbance, morbidity, mortality, sexual and substance associated...

Data from a survey distributed to all full-time faculty in academic departments of psychiatry were used to examine possible sex differences in research activities and rank attainment among psychiatrists. A total of 1923 psychiatrists responded, 1564 men (81.3%) and 359 women (18.7%). Continuous dependent variables were analyzed by using analyses of covariance with the year graduated from medical school as a covariate. For categorical dependent variables, the sample was divided into four 10-year cohorts based on the year graduated from medical school, and differences between men and women were analyzed with chi 2 tests. Over the entire sample, men were more likely than women to have had research training, to have ever been principal investigators on peer-reviewed grants, to mentor research trainees, to be currently involved in research activities, and to meet defined criteria as a "researcher." Many gender differences remained significant after controlling for seniority and research training. In every cohort, the men had attained higher academic rank than the women. In general, differences in research activity and productivity were most marked in the youngest cohort. To ensure a rich talent pool for psychiatric research, efforts must be made to recruit and support researchers from among the increased number of women in psychiatry.

Bayesian modeling of joint and conditional distributions

Objectives The purposes of this study were to investigate the attitudes toward physical education and physical activity levels of middle school students in Jiangxi Province, China, and explore the relationship between these two factors. Methods The subjects consisted of 722 middle school students (male: 371 and female: 351) from 7th to 9th grade at four public middle schools in Jiangxi Province, China. The measurement tools were used the Chinese version of Students' Attitude Toward Physical Education (Hu et al., 2014) and the Chinese version of Physical Activity Questionnaire for Adolescents (Li, 2015). For data analysis, confirmatory factor analysis (CFA), descriptive statistics, univariate analysis of variance (ANOVA), multivariate analysis of variance (MANOVA) were performed, using SPSS 26 and AMOS 27 statistical program. Results The results showed that first, participants' attitudes toward physical education were generally positive across all grades and genders, with average scores above 3.0 for all sub-factors. According to the result of MANOVA, gender had a significant impact on all dependent variables [CE: F(1, 716)=21.795, p<.05; CU: F(1, 716)=14.818, p<.05; TE: F(1, 716)=18.150, p<.05; TU: F(1, 716)=8.130, p<.05]; however, grade did not significantly affect attitudes. Second, physical activity levels varied by gender and grade, with males generally exhibiting higher (2.34) scores than females (1.88). According to a multivariate analysis of variance (MANOVA), both gender [F(1, 716)=80.342, p＜.05] and grade [F(2, 716)=24.351, p＜.05) had significant effects on physical activity scores, while the interaction effect between grade and gender was not significant [F(2, 716)=1.659, p＞.05]. Third, correlation analysis revealed slightly positive relationships between physical activity and the four sub-scales of attitude [CE (r=.290, p<.05); CU (r=.299, p<.05); TE (r=.326, p<.05); TU (r=.283, p<.05)]. Conclusions The results of this study are expected to enhance the understanding of middle school students by schools and physical education teachers for the development of physical education in China, and to contribute to the development of future physical education programs by providing theoretical evidence.

In obesity research it is common to have repeated measures on subjects. Traditional statistical analyses of repeated measures data are analysis of variance (ANOVA) for random effects, and multivariate analysis of variance (MANOVA). Each assume that every subject was measured (i) the same number of times, and (ii) at the same time points. Another typical complication of many research designs is the presence of time-varying covariates. The usual ANOVA approach to repeated measures does not allow such covariates, and the MANOVA approach usually treats them as dependent variables. Hierarchical linear models deal with all of the above issues in a natural manner, making them an important tool for obesity research. This paper discusses some simple hierarchical models, and shows their application using two real data sets.

Work-related stress and depression among physicians pursuing postgraduate training in emergency medicine: An international study

Analyses and Clarifications" published in aggressive behavior (

Back to table of contents Previous article Next article LetterFull AccessLetterRonald E. Hellman M.D.Eileen Klein Ph.D.Thomas Uttaro Ph.D.Ronald E. Hellman M.D.Search for more papers by this authorEileen Klein Ph.D.Search for more papers by this authorThomas Uttaro Ph.D.Search for more papers by this authorPublished Online:1 Apr 2008https://doi.org/10.1176/ps.2008.59.4.447AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InEmail Update on a Program for LGBT Persons With Major Mental IllnessTo the Editor: There is little documentation in the literature on culturally focused services for lesbian, gay, bisexual, and transgendered (LGBT) persons with major mental illness, despite the unique sociocultural issues and identities that they bring into long-term mental health care settings ( 1 , 2 ). We report here on a sample of individuals attending a culturally focused program for LGBT patients with a diagnosis of major mental illness. Participants attended the Rainbow Heights Club (RHC) in Brooklyn, New York ( 3 ), which was created in 2002 in association with the LGBT Affirmative Program of South Beach Psychiatric Center in Brooklyn ( 4 ). Seventy-five individuals were assessed during May and June 2006. After informed consent was obtained, participants completed a multiple-choice questionnaire measuring level of participation and impact of the program. Data were analyzed through response frequencies and multivariate analysis of variance (MANOVA). Study participants had been in psychiatric treatment an average of 16 years. The percentages reported here are based on the number of participants who completed each item. Among the 69 participants who completed the item about diagnosis, affective disorder was the most common diagnosis (32 participants, or 46%), followed by psychotic disorders (24 participants, or 35%), anxiety disorders (seven participants, or 10%), and other disorders (six participants, or 9%). Information about medical conditions and about substance abuse was available for 72 participants. Thirty-six (50%) reported having significant medical conditions. Three (4%) admitted to current abuse of alcohol or other drugs.Of the 73 participants who answered the question about duration of program attendance, 31 (43%) had attended for more than two years, 22 (30%) had attended for one to two years, and 20 (27%) had attended for less than a year. Thirty-four (47% of 72 respondents) attended more than once a week, and 13 (18%) attended less than once a month. Fifty-five participants (76% of 72 respondents) stated that they found the RHC program very helpful. Thirty-six participants (54% of 67 respondents) reported being more adherent to their mental health treatment because of their involvement in the RHC. Fifty-three participants (80% of 66 respondents) reported that their psychiatric symptoms were better or much better since they began attending the RHC. Forty-one (61% of 67 respondents) reported that their relationships were better or much better since they began attending, and 26 (39%) said that their relationships were the same as before program entry.Thirty-six participants (51% of 70 respondents) reported spending time with other members outside the club, and 66 (92% of 72 respondents) reported that it was somewhat or very helpful to think about the club when they were not there. Fifty-three participants (78% of 68 respondents) reported better or much better self-esteem since they began attending RHC. Forty-three participants (63% of 68 respondents) reported better or much better ability to manage stress, and 53 (78% of 68 respondents) reported that their sense of hope was improved or much improved. The MANOVA tested the relationship between five independent variables (substance abuse, helpfulness of the RHC, spending time with members outside RHC, sexual identity, and age) and five dependent variables (symptom improvement, relationships, self-worth, stress, and sense of hope and purpose). A significant association was found between spending time with RHC members outside the club and the dependent variables (Wilks' λ =.719, F=3.360, df=5 and 43, p<.012). The between-subjects test indicated a significant association between spending time with RHC members outside the club and a general improvement in social relationships since joining the RHC (F=5.68, df=1 and 1, p<.021). These findings indicate that the members of a culturally focused program for LGBT individuals with major mental illness experienced improvements in symptoms, mental well-being, and socialization. Further research is necessary to validate these findings and to determine whether they are causally related to specific program elements and why program members benefit. Studies of this minority population are rare and have been limited by small samples. These preliminary findings hold promise for culturally sensitive LGBT programs for persons from sexual minority groups who have chronic and disabling psychiatric disorders.Acknowledgments and disclosuresThe authors report no competing interests.The authors are affiliated with South Beach Psychiatric Center, Brooklyn, New York.