Multi-level Data Modeling (MLM)

On 09.14.10, In statistics, By Dan Calloway

by DAN CALLOWAY
Published 14 September 2010

WEAVERVILLE, NC – Multilevel modeling (MLM) is arguably one of the two most widely employed means of statistical analysis used primarily in the fields of social and behavioral research (Vogt, 2007)⁠. Although MLM has been widely used in sociology, its use in education is also widely known and accepted. In the field of educational research, it is referred to as hierarchical linear modeling (HLM). Other labels used to describe MLM are: random effects models, mixed effects models (used primarily in economics), and random coefficient regression models and covariance components models (Vogt, pp. 214 – 215).

The kinds of research that lend themselves well to MLM are educational and sociological research. A hypothetical study that I propose for use in a two-level MLM is that of modeling students’ academic achievement in reading comprehension in high school within geographical regions of the U.S. At level one, the student’s individual characteristics, such as personality traits, skills, attention span, and parental support would need to be modeled. Likewise, at level two, the geographical regions of the U.S. where the students attend high school, such as North, South, East, Northeast, Midwest, and West would be identified as well. Thus, the independent variables in the study would be personality traits, skills, attention span, parental support, and geographical location of high school attendance in the U.S. The dependent or outcome variable would be academic achievement in reading comprehension. The hierarchical structure of the data is justified in this two-level MLM because the first level of variables under the study are the individual student characteristics that vary within the students themselves, and the variables in the second level would be the area of the U.S. where the students attend high school, which operate separately from the variables that make up the students’ individual characteristics.

In the two-level MLM study proposed, the structure would consist of two separate levels: (1) individual students at level one (and associated characteristics), and (2) geographical region within the U.S. where the students attend high school. At level one, the IV of personality trait would consist of labels 1 = introvert, 2 = extrovert, 3 = motivated, and 4 = non-motivated. The IV of skills would consist of the labels 1 = beginner, 2 = intermediate, and 3 = advanced. The IV of attention span would be given the labels of 1 = can concentrate on any given task for more 10 minutes or less, and 2 = can concentrate on any given task for more than 10 minutes. And, finally, the IV of parental support would be labeled as 1 = full parental support, 2 = some parental support, 3 = no parental support. At level two, the IV of geographical region would be 1 = North, 2 = South, 3 = East, 4 = West, 5 = Northeast, and 6 = Midwest. The outcome or criterion variable of academic achievement in reading comprehension would be labeled as 1 = Poor, 2 = Fair, 3 = Good, and 4 = Excellent.

Reference:

Vogt, W. P. (2007). Quantitative Research Methods for Professionals (Custom., p. 334). Boston, MA: Allyn & Bacon.

Wikio
Wikio
Tagged with: • • •
 
4 Comments
Please Leave A Response

Regression Analysis

On 08.29.10, In statistics, By Dan Calloway

by DAN CALLOWAY
Published on 29 August 2010

WEAVERVILLE, NC – Regression analysis is a statistical process used to examine why an independent variable does not fully explain or predict the dependent variable in a study whereby the researcher looks to answer three basic questions of what is: (1) the total contribution of all independent variables together, (2) the comparative importance of the different variables, and (3) the role a particular independent variable plays mutually exclusive of the effects that other independent variables have on the dependent or outcome variable (Vogt, 2007, p. 145; p. 147). The role of the researcher in using regression analysis is to decide whether to use all the predictor or independent variables to make predictions of the dependent variable or whether to explain the separate effects of the independent variables in making the predictions of the dependent variable; that is, the questions that researchers ask of regression analyses are shaped by the goals of their research and not be the technicalities or complexities of their computations (Vogt, p. 147).

Giving consideration to Project 2, I would use regression analysis to answer the three basic questions discussed earlier. Regression analysis would be used to determine the total contributions of all the independent variables taken together in my problem statement under consideration or study, to identify the comparative importance of the different variables chosen, and to investigate the role of each predictor variable in predicting the outcome variable when examined mutually exclusively of the effects of the other identified predictor variables on the outcome variable. In my regression analysis, the decision as to the independent variables and the dependent variable would be predicated on which variables were predictors and which variable(s) were outcomes in the analysis or problem statement. Those variables identified as predictors or whose values were allowed to vary independently would be selected as the independent variables (IVs) and the variable(s) that were dependent on the effects of the predictors would be classified as the (DVs) or dependent or outcome variable(s).

When conducting research, the researcher could reasonably assume that important variables (such as mediating variables) have been omitted from consideration of the problem under study if the effects of the existing predictor variables were not able to fully explain the outcome or criterion variable. The use of regression analysis is a good means of determining that important variables may have been omitted from the research especially if the regression coefficient of the focus IV is less than the regression coefficient with controls or controls with mediators are added. If the current predictor variables are inadequate to explain the effects on the outcome variable, then it can be logically assumed that there are other predictor variables as yet unidentified that are playing a role either through their interaction with other independent variables or their own direct effect on the outcome variable (Vogt, 2007).

Thus, the research problem I have identified is: “I would like to investigate whether there is a positive correlation between sexual and physical abuse of a child in his/her early childhood development and whether s/he was raised in a loving or abusive single-parent or traditional mixed parental environment, and the propensity of the child to become a criminal outcast in his/her adolescent or adult life as viewed by society.” The independent or predictor variables identified are: environmental upbringing, gender, ethnicity, age, and parental guidance. The outcome or criterion variable identified is adolescent or adult criminal affiliation.

Reference:

Vogt, W. P. (2007). Quantitative Research Methods for Professionals (Custom., p. 334). Boston: Pearson Education, Inc.

Wikio
Wikio
Tagged with: • •
 
0 Comments
Please Leave A Response

Suppressor Variables

On 08.02.10, In blogging, statistics, By Dan Calloway

by DAN CALLOWAY
Published 2 August 2010

WEAVERVILLE, NC – For the purposes of this discussion, I will explore the direct effect of education on political attitudes, the indirect effect of income on political attitudes, and defend my consideration of one over the other. For this article, we will assume that education has been identified as the predictor variable and political attitude is viewed as the criterion variable. The effect of income on the criterion variable is seen as an indirect effect attributed to income known as the suppressor variable rather than a mediator variable. Conger and Jackson (1972) indicates that there is considerable disagreement on what constitutes a suppressor variable and that there has been little research in the manner of relating suppressor variables to the more well known partial correlation and moderator variable. Confusion surrounding the precise definition of a suppressor variable stems from a reinterpretation and relaxing of the Horst (1941) definition, which contained its mode of operation and its mathematical foundation. The classical definition of a suppressor variable provided by Conger and Jackson is a variable “wholly uncorrelated with the criterion, but which, by virtue of a correlation with the predictor, improves the prediction of the criterion” (p. 581). The paradoxical quality of the suppressor variable is that it is possible to increase the prediction of the criterion by utilizing a variable that has a negligible correlation with the criterion, provided that it does correlate with another variable that correlates well with the criterion. To further illustrate this concept, one need examine the prediction in the success of WWII pilot training programs as relayed in Horst (1966, p. 355), in which a battery of tests were given to pilots to evaluate their mechanical, numerical, spatial, and verbal abilities. Noteworthy here is that the first three predictor variables had positive correlations to the criterion variable but the last, verbal ability, had virtually no correlation to the criterion, yet had high correlations with each of the first three predictor variables.

Bobo and Licari (1989) sought to examine the positive relationship between education and political tolerance. The authors identified that one of the more prominent explanations for the positive relationship between education and political tolerance is the enhanced cognitive sophistication on the part of the learner brought about by the additional years of higher education. Through their secondary research into the direct measure of cognitive sophistication as a predictor of political tolerance (a more quantifiable criterion variable), they discovered that cognitive sophistication is the mediating variable or mediating link between education and political tolerance. What Bobo and Licari were able to show was that cognitive sophistication largely mediates the relationship between education and political tolerance above and beyond the moderating variables of age, gender, race, religion, urbanicity, and ideology.

Therefore, I would choose to examine the direct effect of the predictor variable, education, on political attitudes (or tolerance) by first determining whether there is a direct correlation between the suppressor variable, income, and the predictor variable, education. As pointed out in Lubin (1957)⁠ if a high correlation can be shown between the suppressor variable and the predictor variable, then the multiple correlation could be increased significantly. Thus, by demonstrating that a positive correlation between education and income exists, one could then significantly increase the likelihood that there is a positive correlation between education and political tolerance through multiple correlation. The study conducted by Bobo and Licari (1989) helps to reinforce this direct relationship between the predictor variable and the criterion for this discussion.

References:

Bobo, L., & Licari, F. (1989). Education and political tolerance: Testing the effects of cognitive sophistication and target group effect. Public Opinion Quarterly, 53(3), 285-308.

Conger, A., & Jackson, D. (1972). Suppressor variables, prediction, and the interpretation of psychological relationships. Educational and Psychological Measurement, 32(3), 579-599.

Horst, P. (1941). The prediction of personal adjustment. New York, NY.

Horst, P. (1966). Psychological measurement and prediction. Belmont, California: Wadsworth.

Lubin, A. (1957). Some formulae for use with suppressor variables. Educational and Psychological Measurement, 17(2), 286-297.

Dan Calloway

Wikio
Wikio
Tagged with: • •
 
2 Comments
Please Leave A Response

Go To Top »
Get Adobe Flash player

SEO Powered by Platinum SEO from Techblissonline