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 Program: HLM 7 Hierarchical Linear and Nonlinear Modeling Authors: Stephen Raudenbush, Tony Bryk, & Richard Congdon Publisher: Scientific Software International, Inc. (c) 2010 techsupport@ssicentral.com www.ssicentral.com
 Module: HLM2.EXE (7.01.21202.1001) Date: 3 October 2017, Tuesday Time: 11:56: 6

## Specifications for this HLM2 run

Problem Title: no title

The data source for this run = mathread.mdm
The command file for this run = C:\Users\mcrdz\AppData\Local\Temp\whlmtemp.hlm
Output file name = C:\Users\mcrdz\Desktop\DocumentsMCR\COURSES\EPSY8268-HLM\Data\hlm2.html
The maximum number of level-1 units = 2700
The maximum number of level-2 units = 47
The maximum number of iterations = 100

Method of estimation: restricted maximum likelihood

The outcome variable is MATH05

### Summary of the model specified

#### Level-1 Model

MATH05ij = β0j + β1j*(READ05ij) + rij

#### Level-2 Model

β0j = γ00 + u0j
β
1j = γ10 + u1j

READ05 has been centered around the group mean.

#### Mixed Model

MATH05ij = γ00
+ γ

Run-time deletion has reduced the number of level-1 records to 2657

## Final Results - Iteration 16

Iterations stopped due to small change in likelihood function

σ2 = 638.64469

τ

 INTRCPT1,β0 113.088 0.3177 READ05,β1 0.3177 0.00809

τ (as correlations)

 INTRCPT1,β0 1 0.332 READ05,β1 0.332 1

 Random level-1 coefficient Reliability estimate INTRCPT1,β0 0.898 READ05,β1 0.446

The value of the log-likelihood function at iteration 16 = -1.241953E+004

#### Final estimation of fixed effects:

 Fixed Effect Coefficient Standard error t-ratio Approx. d.f. p-value For INTRCPT1, β0 INTRCPT2, γ00 664.288258 1.636901 405.821 46 <0.001 For READ05 slope, β1 INTRCPT2, γ10 0.715466 0.019615 36.475 46 <0.001

#### Final estimation of fixed effects (with robust standard errors)

 Fixed Effect Coefficient Standard error t-ratio Approx. d.f. p-value For INTRCPT1, β0 INTRCPT2, γ00 664.288258 1.619366 410.215 46 <0.001 For READ05 slope, β1 INTRCPT2, γ10 0.715466 0.019368 36.940 46 <0.001

#### Final estimation of variance components

 Random Effect Standard  Deviation Variance  Component d.f. χ2 p-value INTRCPT1, u0 10.63427 113.08760 46 544.14582 <0.001 READ05 slope, u1 0.08996 0.00809 46 94.72818 <0.001 level-1, r 25.27142 638.64469

#### Statistics for current covariance components model

Deviance = 24839.068399
Number of estimated parameters = 4