Comparison Of Multilevel Model And Its Statistical Diagnostics

NOV 4, 2019

Research paper

Comparison of multilevel model and its statistical diagnostics Tags: Statswork | Linear Regression Models | Multilevel model | Statistical diagnostics | Programmers | Statistical Data Analysis | Data Analysis Services Research Planing | Data Collection | Semantic Annotation | Consumer & Retail Analytics | Econometrics

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STATISTICAL DIAGNOSTICS

Diagnostics in statistical analysis is atmost important because there may be few influential observations which may distort the inference of the problem statement at hand.

All influential observations are not outliers, but some outliers are influential.

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MULTILEVEL DATA AND ITS DIAGNOSTICS Multi-level models are the statistical models of parameters (like in usual linear regression model) that vary at more than one level.

Referred with many terms, namely, mixed-effect models, random effect model, hierarchical models and many more.

With the advent of statistical software and computations, multi-level or hierarchical models are widely used for longitudinal repeated measures analysis and in many meta data applications.

Multi-level models also applicable for non-linear case too by using appropriate Generalized Linear Mixed Models.

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TABLE:1 FIXED EFFECT MODEL USING REGRESSION

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TABLE:2 RANDOM EFFECT MODEL USING REGRESSION

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TABLE:3 HIERARCHICAL MODEL

Like in linear regression model, the mixed model also must satisfies the assumptions of the model.

If any one of the assumptions is violated, then the data is taken to the diagnostics part of the model.

Mostly, researchers checks the data for the independence. If it gets violated, then the most popular residual diagnostics is carried out to identify the influential or outlier points which deviate from other.

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TABLE:4 LINEAR REGRESSION BETWEEN ATTRACTIVENESS AND PURCHASE INTENTION

TABLE:5 R, R-SQUARE AND ADJUSTED RSQUARE

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TABLE:6 RESIDUALS OF LINEAR REGRESSION

• Residual diagnostics in the multilevel models needs careful attention.

• Usually statistical analysis practitioner prefer to fit a level 1 (with one independent variable) regression model with and without the influential points and compare the plots of the residuals.

Later to fit level 2 regression model and cross check the results.

• Bootstrapping technique with jacknife residuals can also be useful in diagnosing the multi-level model for greater accuracy.

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TABLE:7 MULTIPLE REGRESSION ANALYSIS TO PREDICT ONE DEPENDENT VARIABLE BASED ON MORE THAN ONE INDEPENDENT VARIABLE

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SOFTWARE PACKAGES IN R FOR DIAGNOSING MULTI-LEVEL MODEL Used for linear mixed model diagnostics.

Misspecification is a major problem when using usual residual statistics such as Pearson and Response in the multi-level modelling.

Residplo t Used for the diagnostics for hierarchical models.

a Unusual pattern in the data are identified using the residual vs the predicted plots.

di a H LM

M AR DH

Overcomes the drawback of residplot package and gives a straightforward method as in linear regression models.

g

Used for residual diagnostics of GLMMs.

Provides deletion diagnostics with the help of distance based metrics such as Cook’s distance, COVratio, COVtrace and MDFFITS. Allows the user to obtain the residuals through least square estimates or bayes estimates. Also allows the user to obtain various residuals using marginal, conditional distributions.

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OTHER MULTI-LEVEL MODELS

Diagnostic tools for random effects model with an application to growth curve modelLindsey and Lindsey (2000).

01 02

Case deletion diagnostics in multilevel models for identifying the influential observations in the data- Shi and Chen (2008).

Diagnostics for multilevel models in a more concrete way- Snijders and Berkhof (2007).

03

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SUMMARY There have been a lot of applications emerging for multilevel regression models especially in the meta data and it became a common practice in the field of statistics to make the model more accurate. Thus, more appropriate diagnostic measures are to be selected with the suitable model in validating the multi-level regression results with greater accuracy.

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