# ΟΙ ΣΥΝΕΡΓΑΤΕΣ ΠΟΥ

## ΣΥΜΒΑΛΛΟΥΝ ΕΝΕΡΓΑ ΣΤΗΝ ΕΠΙΤΥΧΙΑ

 HLM - Hierarchical Linear and Nonlinear Modeling (HLM)

In social research and other fields, research data often have a hierarchical structure. That is, the individual subjects of study may be classified or arranged in groups which themselves have qualities that influence the study. In this case, the individuals can be seen as level-1 units of study, and the groups into which they are arranged are level-2 units. This may be extended further, with level-2 units organized into yet another set of units at a third level and with level-3 units organized into another set of units at a fourth level. Examples of this abound in areas such as education (students at level 1, teachers at level 2, schools at level 3, and school districts at level 4) and sociology (individuals at level 1, neighborhoods at level 2). It is clear that the analysis of such data requires specialized software. Hierarchical linear and nonlinear models (also called multilevel models) have been developed to allow for the study of relationships at any level in a single analysis, while not ignoring the variability associated with each level of the hierarchy.

The HLM program can fit models to outcome variables that generate a linear model with explanatory variables that account for variations at each level, utilizing variables specified at each level. HLM not only estimates model coefficients at each level, but it also predicts the random effects associated with each sampling unit at every level. While commonly used in education research due to the prevalence of hierarchical structures in data from this field, it is suitable for use with data from any research field that have a hierarchical structure. This includes longitudinal analysis, in which an individual's repeated measurements can be nested within the individuals being studied. In addition, although the examples above implies that members of this hierarchy at any of the levels are nested exclusively within a member at a higher level, HLM can also provide for a situation where membership is not necessarily "nested", but "crossed", as is the case when a student may have been a member of various classrooms during the duration of a study period.

The HLM program allows for continuous, count, ordinal, and nominal outcome variables and assumes a functional relationship between the expectation of the outcome and a linear combination of a set of explanatory variables. This relationship is defined by a suitable link function, for example, the identity link (continuous outcomes) or logit link (binary outcomes).

 New in HLM 7

HLM 7 offers unprecedented flexibility in modeling multilevel and longitudinal data. With the same full array of graphical procedures and residual files along with the speed of computation, robustness of convergence, and user-friendly interface of HLM 6, HLM 7 highlights include three new procedures that handle binary, count, ordinal and multinomial (nominal) response variables as well as continuous response variables for normal-theory hierarchical linear models:

Four-level nested models:

• Four-level nested models for cross-sectional data (for example, models for item response within students within classrooms within schools).
• Four-level models for longitudinal data (for example items within time points within persons within neighborhoods).

Four-way cross-classified and nested mixtures:

• Repeated measures on students who are moving across teachers within schools over time, or item responses nested within immigrants who are cross-classified by country of origin and country of destination.
• Repeated measures on persons who are simultaneously living in a given neighborhood and attending a given school.

Hierarchical models with dependent random effects:

• Spatially dependent neighborhood effects.
• Social network interactions.

HLM 7 also offers new flexibility in estimating hierarchical generalized linear models through the use of Adaptive Gauss-Hermite Quadrature (AGH) and high-order Laplace approximations to maximum likelihood. The AGH approach has been shown to work very well when cluster sizes are small and variance components are large. the high-order Laplace approach requires somewhat larger cluster sizes but allows an arbitrarily large number of random effects (important when cluster sizes are large)

New HTML output that supplies elegant notation for statistical models including visually attractive tables is also now available, allowing the user to cut and paste output of interest into manuscripts.

 HLM 7 manual
• A hard copy of the HLM 7 manual is not available.
• PDF copies of the HLM 7 manual are available via the HLM 7 Manual option on the Help menu of the full, rental, trial, and student editions of HLM 7 for Windows.

# Overview of modeling options in the HLM statistical applications

 Interface option HLM2 HLM3 HLM4 HMLM HMLM2 HCM2 HCM3 HLMHCM Basic Settings: Distribution of outcome Normal outcome Y Y Y Y Y Y Y Y Bernoulli outcome Y Y Y - - Y Y Y Poisson outcome (constant exposure) Y Y Y - - Y Y Y Poisson outcome (variable exposure) Y Y Y - - Y Y Y Binomial outcome Y Y Y - - Y Y Y Multinomial outcome Y Y - - - - Ordinal outcome Y Y - - - - Over-dispersion Y Y Y - - Y Y Y Basic Settings: Residual files, title and file names Residual file at all levels Y Y Y - - Y Y Y Title Y Y Y Y Y Y Y Y Output filename Y Y Y Y Y Y Y Y Graph filename Y Y Y Y Y Y - - Basic Settings: Treatment of level-1 variance Unrestricted - - - Y Y - - - Skip unrestricted - - - Y Y - - - Homogeneous - - - Y Y - - - Heterogeneous - - - Y Y - - - Log-linear - - - Y Y - - - Predictor of level-1 var - - - Y Y - - - 1-st order autoregressive - - - Y Y - - - Iteration Settings Number of  iterations Y Y Y Y Y Y Y Y Frequency of accelerator Y Y Y Y Y Y Y Y % change to stop iterating Y Y Y Y Y Y Y Y How to handle bad variance-covariance matrix Y Y Y Y Y Y Y Y What to do when convergence not reached Y Y Y Y Y Y Y Y Mode of acceleration Y Y - - - - - - Estimation Settings REML Y - - - - - - - FML Y Y Y Y Y Y Y Y PQL Y Y - - - Y Y - (HGLM) (HGLM) LaPlace 6 Y Y - - - - - - (HGLM) (HGLM) EM Laplace Y - - - - - - - (HGLM) Adaptive Gaussian Quadrature Y Y - - - - - - Constraint of fixed effects Y Y - - - - - - Heterogeneous sigma^2 Y - - - - - - - Plausible values Y Y - - - - - - Multiple imputation Y Y - - - - - - Latent variable regression Y Y - Y Y - - - Design weighting Y Y - - - Y Y - Precision weighting (v-known) Y Y - - - - - - Level-1 deletion variables Y Y Y - - Y Y Y Fix sigma^2 to specified value Y Y Y Y Y Y Y Y Spatial dependence Y - - - - - - Y Hypothesis Testing Multivariate hypothesis tests Y Y Y Y Y Y Y Y Deviance of models comparison Y Y Y Y Y Y Y Y Test homogeneity of level-1var Y - - - - - - - Output Settings No of OLS estimates shown Y - - - - - - - Reduced output Y Y Y Y Y Y Y Y Print variance-covariance matrices Y Y - Y Y - - - Exploratory Analysis (level-2) Y Y - - - - - - Exploratory Analysis (level-3) - Y - - - - - - Graph Equations (model based) Model graphs Y Y Y Y Y Y - - Level-1 equation graphing Y Y - - - - - - Level-1 residual box-whisker plots Y Y - - - - - - Level-1 residual vs predicted values Y Y - - - - - - Level-2 EB/OLS coefficient confidence intervals Y Y - - - - - - Graph Data line plots, scatter plots Y Y - - - - - - box-whisker plots Y Y - - - - - -

 HLM 7 is Compatible with Windows 8. It has been tested on Windows 8 and no problems were reported.
 HLM 7 is Compatible with Windows 7. It has successfully passed Microsoft designed tests for compatibility and reliability on Windows 7. It can be used on both the 32-bit and 64-bit editions. Compatible with Windows 7 products install without worry and run reliably with Windows 7.
 Microsoft has awarded SSI's HLM software its prestigious Certified for Windows Vista logo. Only applications that pass rigorous testing procedures for compatibility, functionality, and reliability on Windows Vista-based personal computers are granted this logo.

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