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# Multilevel Modeling - PowerPoint PPT Presentation

Multilevel Modeling. 1. Overview 2. Application #1: Growth Modeling Break 3. Application # 2: Individuals Nested Within Groups 4. Questions?. Overview. What is multilevel modeling? Examples of multilevel data structures Brief history Current applications

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## PowerPoint Slideshow about ' Multilevel Modeling' - samson-allison

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Presentation Transcript

1. Overview

2. Application #1: Growth Modeling

Break

3. Application # 2: Individuals Nested Within Groups

4. Questions?

• What is multilevel modeling?

• Examples of multilevel data structures

• Brief history

• Current applications

• Why multilevel modeling?

• What types of studies use multilevel modeling?

• Computer Programs (HLM 6

SAS Mixed

• Resources

• What effects do the following variables have on 3rd grade reading achievement?

School Size

Classroom Climate

Student Gender

Nested Data Structures

• 1. Individuals Nested Within Groups

### Individuals Undivided

Unit of Analysis = Individuals

Unit of Analysis = Individuals + Classes

Unit of Analysis = Individuals + Classes + Schools

• Neighborhoods are nested within communities

• Families are nested within neighborhoods

• Children are nested within families

• Schools are nested within districts

• Classes are nested within schools

• Students are nested within classes

Level 4 District (l)

Level 3 School (k)

Level 2 Class (j)

Level 1 Student (i)

2nd Type of Nesting

• Repeated Measures Nested Within Individuals

Focus = Change or Growth

Carlos

Day Energy Level

Monday = 0 98

Tuesday = 1 90

Wednes. = 2 85

Thursday = 3 72

Friday = 4 70

3rd Type of Nesting (similar to the 2nd)

• Repeated Measures Nested Within Individuals

Focus is not on change

Focus in on relationships between variables within an individual

Carlos

Day Hours of SleepEnergy Level

Monday 9 98

Tuesday 8 90

Wednesday 8 85

Thursday 6 72

Friday 7 70

Level 2 Student (i)

Level 1 Repeated Measures

Over Time (t)

• Data nested within a group tend to be more alike than data from individuals selected at random.

• Nature of group dynamics will tend to exert an effect on individuals.

• Intraclass correlation (ICC) provides a measure of the clustering and dependence of the data

0 (very independent) to 1.0 (very dependent)

Details discussed later

Brief Historyof Multilevel Modeling

Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. Sociological Review, 15, 351-357.

Burstein, Leigh (1976). The use of data from groups for inferences about individuals in educational research. Doctoral Dissertation, Stanford University.

Frequency of HLM application evidenced in Scholarly Journals

• Growth Curve Analysis

• Value Added Modeling of Teacher and School Effects

• Meta-Analysis

Extension of General Linear Modeling

Simple Linear Regression

Multiple Linear Regression

ANOVA

ANCOVA

Repeated Measures ANOVA

• Our focus will be on observed variables (not Latent Variables as in Structural Equation Modeling)

• Individual level analysis (ignore group)

• Group level analysis (aggregate data and ignore individuals)

• Individual level analysis (ignore group)

Violation of independence of data assumption leading to misestimated standard errors (standard errors are smaller than they should be).

• Group level analysis

(aggregate data and ignore individuals)

Aggregation bias = the meaning of a variable at Level-1 (e.g., individual level SES) may not be the same as the meaning at Level-2 (e.g., school level SES)

• 2 or more levels can be considered simultaneously

• Can analyze within- and between-group variability

Quantitative

Experimental

*Nonexperimental

(Survey, Observational)

2 or 3 levels very common

15 students x 10 classes x 10 schools

= 1,500

• Continuous Scale (Achievement, Attitudes)

• Binary (pass/fail)

• Categorical with 3 + categories

SPSS Users

2 SAV Files: Level 1

Level 2

(Raudenbush, Bryk, Cheong, & Congdon, 2004)

SAS Users

Proc Mixed

Resources (Sample…see handouts for more complete list)

• Books

• Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd ed. Raudenbush & Bryk, 2002.

• Introducing Multilevel Modeling.

Kreft & DeLeeum, 1998.

• Journals

• Educational and Psychological Measurement

• Journal of Educational and Behavioral Sciences

Resources (cont)(Sample…see handouts for more complete list)

• Software

• HLM6

• SAS (NLMIXED and PROC MIXED)

• MLwiN

• Journal Articles

• See Handouts for various methodological and applied articles

• Data Sets

• NAEP Data

• NELS:88; High School and Beyond

• A teacher with 1 classroom of 24 students used weekly curriculum-based measurements to monitor reading over a 14 week period. The teacher was interested in individual students’ rates of change and differences in change by male and female students.

• How would you classify this situation?

(a) not multilevel

(b) 2-level

(c) 3-level

• A researcher randomly selected 50 elementary schools and randomly selected 30 teachers within each school. The researcher was interested in the relationships between 2 predictors (school size and teachers’ years experience at their current school) and teachers’ job satisfaction.

• How would you classify this situation?

(a) not multilevel

(b) 2-level

(c) 3-level

• 60 undergraduates from the research participant pool volunteered for a study that used written vignettes to manipulate the interactional style (warm, not warm) of a professor interacting with a student.  30 randomly assigned students read the vignette depicting warmth and 30 randomly assigned students read the vignette depicting a lack of warmth.  After reading the vignette students used a questionnaire to rate the likeability of the professor.

• How would you classify this situation?

(a) not multilevel

(b) 2-level

(c) 3-level

(Select ONLY one)

• Studying the growth in reading achievement over a two year period

• Studying changes in student attitudes over the middle school years

• What is the form of change for an individual during the study?

• What is an individual’s initial status on the outcome of interest?

• How much does an individual change during the course of the study?

Rise

Run

• What is the average initial status of the participants?

• What is the average change of the participants?

• To what extent do participants vary in their initial status?

• To what extent do participants vary in their growth?

• To what extent does initial status relate to growth?

• To what extent is initial status related to predictors of interest?

• To what extent is growth related to predictors of interest?

• How many waves a data collection are needed?

• >2

• Depends on complexity of growth curve

• Can there be different numbers of observations for different participants?

Examples

• Missing data

• Planned missingness

• Can the time between observations vary from participant to participant?

Example: Students observed

• 1, 3, 5, & 7 months

• 1, 2, 4, & 8 months

• 2, 4, 6, & 8 months

• How many participants are needed?

• More is better

• Power analyses

• > 30 rule of thumb

• How should participants be sampled?

• What you have learned about sampling still applies

• What is the value of random assignment?

• What you have leaned about random assignment still applies

• How should the outcome be measured?

• What you have learned about measurement still applies

• Context description

A researcher was interested in changes in verbal fluency of 4th grade students, and differences in the changes between boys and girls.

IDGender   Time______

t0    t4    t7

1    0  20    30    30

2     0          40    44    49

3 0          45    40    60

4     0         50    55    59

5     0          42    48    53

6 1          45    52    61

7 1          39    55    63

8 1          46    58    68

9 1          44    49    59

• Level-1 model specification

• Level-2 model specification

• Combined Model

• SAS program

procmixed covtest;

class gender;

model score = time gender time*gender/s;

random intercept / sub=student s;

• SAS output – variance estimates

Covariance Parameter Estimates

Standard Z

Cov Parm Subject Estimate Error Value Pr Z

Intercept Student 62.5125 35.9682 1.74 0.0411

Residual 14.1173 4.9912 2.83 0.0023

• SAS output – fixed effects

Solution for Fixed Effects

Standard

Effect Gender Estimate Error DF t Value Pr > |t|

Intercept 39.8103 3.7975 7 10.48 <.0001

time 1.5077 0.3295 16 4.58 0.0003

Gender F 5.7090 5.6962 16 1.00 0.3311

Gender M 0 . . . .

time*Gender F 1.0692 0.4943 16 2.16 0.0460

time*Gender M 0 . . . .

• Graph – fixed effects

• Conclusions

• Fourth grade girl’s verbal fluency is increasing at a faster rate than boy’s.

• Studying attitudes of teachers who are nested in schools

• Studying achievement for students who are nested in classrooms that are nested in schools

• How much variation occurs within and among groups?

• To what extent do teacher attitudes vary within schools?

• To what extent does the average teacher attitude vary among schools?

• What is the relationship among selected within group factors and an outcome?

• To what extent do teacher attitudes vary within schools as function of years experience?

• To what extent does student achievement vary within schools as a function of SES?

• What is the relationship among selected between group factors and an outcome?

• To what extent do teacher attitudes vary across schools as function of principal leadership style?

• To what extent does student math achievement vary across schools as a function of the school adopted curriculum?

• To what extent is the relationship among selected within group factors and an outcome moderated by a between group factor?

• To what extent does the within schools relationship between student achievement and SES depend on the school adopted curriculum?

• Consider a design where students are nested in schools

• How should schools should be sampled?

• How should students be sampled within schools?

• Consider a design where students are nested in schools

• How many schools should be sampled?

• How many students should be sampled per school?

• What kind of outcomes can be considered?

• Continuous

• Binary

• Count

• Ordinal

• How will level-1 variables be conceptualized and measured?

• SES

• How will level-2 variables be conceptualized and measured?

• SES

• Individual growth trajectory – individual growth curve model

• A model describing the change process for an individual

• Intercept

• Predicted value of an individual’s status at some fixed point

• The intercept cold represent the status at the beginning of a study

• Slope

• The average amount of change in the outcome for every 1 unit change in time

• Hierarchical Linear Model

• The hierarchical or nested structure of the data

• For growth curve models, the repeated measures are nested within each individual

• Level 1 = time-series data nested within an individual

• Level 2 = model that attempts to explain the variation in the level 1 parameters

• Fixed coefficient

• A regression coefficient that does not vary across individuals

• Random coefficient

• A regression coefficient that does vary across individuals

• Balanced design

• Equal number of observations per unit

• Unbalanced design

• Unequal number of observation per unit

• Unconditional model

• Simplest level 2 model; no predictors of the level 1 parameters (e.g., intercept and slope)

• Conditional model

• Level 2 model contains predictors of level 1 parameters

• Empirical Bayes (EB) estimate

• “optimal composite of an estimate based on the data from that individual and an estimate based on data from other similar individuals” (Bryk, Raudenbush, & Condon, 1994, p.4)

• Expectation-maximization (EM) algorithm

• An iterative numerical algorithm for producing maximum likelihood estimates of variance covariance components for unbalanced data.