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

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Module:	HLM2.EXE (7.01.21202.1001)
Date:	3 October 2017, Tuesday
Time:	12:28:53

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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

    MATH05_ij = β_0j + β_1j*(READ05_ij) + r_ij

Level-2 Model

    β_0j = γ₀₀ + γ₀₁*(READ05_M_j) + u_0j
    β_1j = γ₁₀ + γ₁₁*(READ05_M_j) + u_1j

READ05 has been centered around the group mean.

READ05_M has been centered around the grand mean.

Mixed Model

    MATH05_ij = γ₀₀ + γ₀₁*READ05_M_j 
    + γ₁₀*READ05_ij + γ₁₁*READ05_M_j*READ05_ij 
     + u_0j + u_1j*READ05_ij + r_ij

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

Final Results - Iteration 21

Iterations stopped due to small change in likelihood function

σ² = 638.85331

τ

INTRCPT1,β0	35.21338	0.44415
READ05,β1	0.44415	0.00876

τ (as correlations)

INTRCPT1,β0	1.000	0.799
READ05,β1	0.799	1.000

 

Random level-1 coefficient	Reliability estimate
INTRCPT1,β0	0.736
READ05,β1	0.464

The value of the log-likelihood function at iteration 21 = -1.240026E+004

Final estimation of fixed effects:

Fixed Effect	Coefficient	Standard error	t-ratio	Approx. d.f.	p-value
For INTRCPT1, β0
INTRCPT2, γ00	664.330346	1.007423	659.436	45	<0.001
READ05_M, γ01	0.634724	0.073370	8.651	45	<0.001
For READ05 slope, β1
INTRCPT2, γ10	0.719806	0.019884	36.200	45	<0.001
READ05_M, γ11	-0.000758	0.001386	-0.547	45	0.587

 

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	664.330346	0.984300	674.927	45	<0.001
READ05_M, γ01	0.634724	0.079260	8.008	45	<0.001
For READ05 slope, β1
INTRCPT2, γ10	0.719806	0.019909	36.154	45	<0.001
READ05_M, γ11	-0.000758	0.001084	-0.699	45	0.488

 

Final estimation of variance components

Random Effect	Standard  Deviation	Variance  Component	d.f.	χ2	p-value
INTRCPT1, u0	5.93409	35.21338	45	178.63670	<0.001
READ05 slope, u1	0.09362	0.00876	45	93.79361	<0.001
level-1, r	25.27555	638.85331

Statistics for current covariance components model

Deviance = 24800.523993
Number of estimated parameters = 4