Post on 25-Dec-2015
An Introduction to HLM and SEM
Carolyn Furlow
Hierarchical Linear Modeling (HLM)Structural Equation Modeling (SEM) Multilevel models or Hierarchical Linear
Models and Structural Equation Models are both considered extensions of regression analyses.
Both are frequently used with educational data and are rapidly gaining in popularity.
When should HLM be used?
HLM is appropriate for use when we have nested data structures which occurs frequently with educational data.
For example, when we have students who are nested in classrooms, classrooms nested within schools, etc…
E.g., if we randomly sampled three classrooms of students from 10 different schools and then collected data from all these students.
Other HLM scenarios with nested data
Clients in groups for group therapy Employees in organizations School administrators in school districts Voters in voting precincts Homeowners in neighborhoods
Unit of Analysis
Researchers have difficulty deciding the appropriate unit of analysis with educational data.
Should the student be the unit of analysis or the classroom mean, school mean, etc.?
HLM simultaneously accounts for several levels of data
HLM uses
We can simultaneously study the effects of group level variables and individual level variables with HLM
There may be interactions across levels as well that only HLM can account for.
For example, the effect of student study time may be related to teacher emphasis on homework.
Why not just use multiple regression?
Students from Classroom A tend to be more alike with each other than they would be with students from Classroom B.
Students within any one classroom, b/c they were taught together tend to be similar in their performance
As a result, they provide less information than if the same number of students had been taught separately by different teachers
Why not just use multiple regression?
Therefore the assumptions of constant variance and independence of errors in multiple regression are violated.
Incorrect standard errors and tests of significance for regression coefficients would be given using MR when HLM should be used.
Example from Tate
Example of a policy analysis related to ongoing school reform efforts in a hypothetical state.
Set of instructional objectives for fifth grade science were developed but individual schools not required to use objectives in their curriculum
Example from Tate
Annual state-wide test was modified to reflect the new objectives
Evidence that individual schools vary with respect to how consistent their science classes are with objectives
Example from Tate
Policy makers have several research questions Question 1 (group level)
Is the average school achievement on the state-wide science test, controlling for student aptitude, related to the degree to which the school science instruction is consistent with the state-wide objectives?
Example from Tate
Question 2 (individual level)Is the relationship between individual science
achievement and individual aptitude within each school related to the degree to which the school science curriculum is consistent with the state-wide objectives?
Hypothetical Study
Random sample of 20 schools from the state Collected measures of individual science
achievement and aptitude for all 580 students in the 20 schools
Each school has also been given a score on a scale reflecting “Degree of Consistency of School Science Instruction with State-Wide Objectives”
Hypothetical Study
We can test at the group level how much the school’s level of consistency affects the variability of school’s scores on the achievement test
We can also test whether the relationship between individual achievement and aptitude is related to how consistent the curriculum is with the objectives
Structural Equation Modeling (SEM)
Also seen as an extension of regression analysis.
SEM attempts to analyze more complicated causal models and can incorporate unobserved (latent) variables and mediating variables as well as observed (measured) variables
SEM involves imposing a theoretical model on a set of variables to explain their relationships.
SEM
Latent variables are unobserved/unobservable variables such as self-esteem, marital happiness, depression. These are sometimes called factors.
They are measured by indicators (observed variables), often behaviors that can be observed such as stated chance of getting divorced, number of fights with spouse in the last week.
SEM
Standard SEM – consists of mediating variables and latent variables
Special Cases of SEMPath analysis - all variables are observed but some
type of mediating variable exists Confirmatory factor analysis - where a latent
variable such as intelligence is measured by several indicator variables
SEM
Obtain overall test of how well our data fits with our proposed model
Also obtain significance values for each of the paths between variables
Example of SEM (path-analytic model)
Authoritative Parenting
Style
Ethnic Identity
Teacher Support
Family Stress
GlobalSelf-esteem
Confirmatory Factor Analysis
SEM