Multiple topics for Advanced Statistical Analysis
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Questions and Answers

What is another name for multilevel modelling?

  • Mixed model (correct)
  • Logistic model
  • Regression model
  • Linear model

What is the variance partition coefficient (VPC) or intraclass correlation coefficient (ICC)?

  • A measure of the variation within higher level units
  • A measure of the variation within lower level units
  • A measure of the variation between higher level units (correct)
  • A measure of the variation between lower level units

When is multilevel modelling not appropriate?

  • When there is no significant variation of the intercept (correct)
  • When the number of groups is very small
  • When only fixed effects are of importance
  • All of the above

What is the main advantage of fixed effects models?

<p>They remove all variation between higher level units from parameter estimation (C)</p> Signup and view all the answers

What is the minimum VPC/ICC value that should not be ignored when analyzing hierarchical data?

<p>5% (D)</p> Signup and view all the answers

What are some examples of multilevel modelling settings?

<p>All of the above (C)</p> Signup and view all the answers

What is the main assumption of multilevel analysis for making causal inferences?

<p>Random allocation of people within the different higher unit levels (D)</p> Signup and view all the answers

What is the main drawback of fixed effects models?

<p>They estimate time-invariant variables on the higher level units (C)</p> Signup and view all the answers

What type of regression models can be extended to multilevel models?

<p>All regression models can be extended to multilevel models (A)</p> Signup and view all the answers

When is multilevel modelling appropriate?

<p>When interested in interaction effects of variables on different levels (B)</p> Signup and view all the answers

What is the main difference between linear regression model with one level and multilevel regression model with two levels?

<p>The number of levels included in the model (A)</p> Signup and view all the answers

What is endogeneity in regression models?

<p>The pollution of the coefficient of the variable of interest (B)</p> Signup and view all the answers

What are instrumental variables?

<p>Variables that are uncorrelated with the variable of interest and the error term (D)</p> Signup and view all the answers

What are the properties of valid instruments?

<p>cov(H, ϵ) ̸= 0 and cov(H, x) = 0 (C)</p> Signup and view all the answers

What is the 2-Stage Least Squares (2SLS) method used for?

<p>To avoid reverse causality in a regression model (A)</p> Signup and view all the answers

What is the first step in the 2SLS method?

<p>Regress the endogenous variable on the instrument (A)</p> Signup and view all the answers

What is the second step in the 2SLS method?

<p>Predict the value of the endogenous variable given the values of the instrument (C)</p> Signup and view all the answers

What is the logistic regression equation used for?

<p>To model the probability of a binary outcome (B)</p> Signup and view all the answers

What is the interpretation of the coefficient in the logistic regression equation?

<p>If x increases with 1 unit, ln(odds) increases with b1 (C)</p> Signup and view all the answers

What is the formula for interpretation polynomials used for?

<p>To interpret the effect of a variable on the dependent variable (D)</p> Signup and view all the answers

What is the interpretation of the slope in the formula for interpretation polynomials?

<p>A linear line increasing in x if b2 is positive (A)</p> Signup and view all the answers

What is the null hypothesis in the Likelihood-Ratio test for logistic regression?

<p>The model with constant only is a better fitting model (C)</p> Signup and view all the answers

What is the Hosmer and Lemeshow test used for in logistic regression?

<p>To test the goodness-of-fit of the logistic regression model (A)</p> Signup and view all the answers

What is the main issue with correlated missing variables in statistical analysis?

<p>It can lead to biased estimates and incorrect conclusions (B)</p> Signup and view all the answers

What is the main issue with sample selection in statistical analysis?

<p>It narrows the interpretation of results to a specific group within the population (A)</p> Signup and view all the answers

What is reverse causality in statistical analysis?

<p>When the independent variable is causing the outcome variable (A)</p> Signup and view all the answers

What are instrumental variables in statistical analysis?

<p>Variables that are correlated with the independent variable but uncorrelated with the error term (B)</p> Signup and view all the answers

What are the properties of valid instruments in statistical analysis?

<p>cov(H, ϵ) = 0 and cov(H, x) ̸= 0 (B)</p> Signup and view all the answers

What is the 2-Stage Least Squares (2SLS) method in statistical analysis?

<p>A method for linear regression models with multiple independent variables (A)</p> Signup and view all the answers

What is the main advantage of the 2-Stage Least Squares (2SLS) method in statistical analysis?

<p>It is not affected by endogeneity (D)</p> Signup and view all the answers

What is the Joint sign F-test in linear regression models?

<p>A test for the overall significance of the model (A)</p> Signup and view all the answers

What is the Maximum likelihood method in logistic regression?

<p>A method for estimating the coefficients of the logistic regression equation (B)</p> Signup and view all the answers

What is the Likelihood-Ratio test in logistic regression?

<p>A test for the goodness of fit of the model (C)</p> Signup and view all the answers

What is the main advantage of the Hosmer and Lemeshow test in logistic regression?

<p>It tests the goodness of fit of the model (B)</p> Signup and view all the answers

What is the formula for interpretation polynomials in statistical analysis?

<p>y = b0 + b1x + b2x^2 (B)</p> Signup and view all the answers

Linear regression models can be used to analyze the relationship ______ independent and dependent variables

<p>between</p> Signup and view all the answers

Logistic regression models are used when the dependent variable is ______ (0 or 1)

<p>binary</p> Signup and view all the answers

Sample selection and correlated missing variables can impact the ______ of regression results

<p>interpretation</p> Signup and view all the answers

Endogeneity can occur when the independent variable is affected by the ______ term

<p>error</p> Signup and view all the answers

2-Stage Least Squares (2SLS) is a method for using ______ variables to address endogeneity

<p>instrumental</p> Signup and view all the answers

OLS joint sign F-test and R-squared values can be used to evaluate the ______ of linear regression models

<p>fit</p> Signup and view all the answers

Maximum likelihood and likelihood ratio tests can be used to evaluate the ______ of logistic regression models

<p>fit</p> Signup and view all the answers

Pseudo R-squared values and the Hosmer and Lemeshow test can also be used to evaluate the ______ of logistic regression models

<p>fit</p> Signup and view all the answers

The interpretation of coefficients in regression models depends on the type of model and the specific ______ included

<p>variables</p> Signup and view all the answers

In linear regression models, the interpretation is based on the change in the dependent variable for a ______-unit increase in the independent variable

<p>one</p> Signup and view all the answers

In logistic regression models, the interpretation is based on the change in the ______ of the dependent variable for a one-unit increase in the independent variable

<p>odds</p> Signup and view all the answers

Polynomial regression models can be used to analyze ______ relationships between variables

<p>non-linear</p> Signup and view all the answers

Study Notes

Introduction to Multilevel Modelling

  • Multilevel modelling corrects for bias in parameters and standard errors by accounting for nesting if one observes the hierarchical structure of the data.
  • Multilevel modelling is also known as mixed model, hierarchical model, random coefficient model, and random effects model.
  • Examples of multilevel modelling settings include people-neighborhoods-regions-countries, workers-departments-organizations-regions-countries, and subjects-different studies.
  • All regression models can be extended to multilevel models if the data allows.
  • Multilevel regression models include linear regression model with one level, linear (fixed effect) regression model with two levels, and multilevel regression model with two levels.
  • The variance partition coefficient (VPC) or intraclass correlation coefficient (ICC) is an important statistic in multilevel modelling. Rule of thumb: Do not ignore the hierarchical structure of the data if VPC/ICC >5%.
  • Multilevel analysis has a strong assumption of random allocation of people within the different higher unit levels for making causal inferences.
  • Fixed effects models remove all variation between higher level units from parameter estimation but have the drawback of not estimating time-invariant variables on the higher level units.
  • Multilevel modelling is appropriate when there is a hierarchical data structure, theoretical setup implies MLM, sample size requirements are met, and when interested in interaction effects of variables on different levels.
  • Multilevel modelling is not appropriate when the number of groups (e.g. spatial units) is very small, there is no significant variation of the intercept (PVC/ICC very small), only fixed effects are of importance, only group-level associations are of interest, or when there is a low number (or non-representative set) of level-1 observations for levels-2 or 3.
  • For a more detailed application of multilevel logistic modelling, study Sommet & Morselli (2017): Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS, International Review of Social Psychology, 30(1), 203-218.
  • For an application in the field of (Economic) Geography, study Srholec (2010): A Multilevel Approach to Geography of Innovation, Regional Studies, 44(9), 1207-1220.

Introduction to Multilevel Modelling

  • Multilevel modelling corrects for bias in parameters and standard errors by accounting for nesting if one observes the hierarchical structure of the data.
  • Multilevel modelling is also known as mixed model, hierarchical model, random coefficient model, and random effects model.
  • Examples of multilevel modelling settings include people-neighborhoods-regions-countries, workers-departments-organizations-regions-countries, and subjects-different studies.
  • All regression models can be extended to multilevel models if the data allows.
  • Multilevel regression models include linear regression model with one level, linear (fixed effect) regression model with two levels, and multilevel regression model with two levels.
  • The variance partition coefficient (VPC) or intraclass correlation coefficient (ICC) is an important statistic in multilevel modelling. Rule of thumb: Do not ignore the hierarchical structure of the data if VPC/ICC >5%.
  • Multilevel analysis has a strong assumption of random allocation of people within the different higher unit levels for making causal inferences.
  • Fixed effects models remove all variation between higher level units from parameter estimation but have the drawback of not estimating time-invariant variables on the higher level units.
  • Multilevel modelling is appropriate when there is a hierarchical data structure, theoretical setup implies MLM, sample size requirements are met, and when interested in interaction effects of variables on different levels.
  • Multilevel modelling is not appropriate when the number of groups (e.g. spatial units) is very small, there is no significant variation of the intercept (PVC/ICC very small), only fixed effects are of importance, only group-level associations are of interest, or when there is a low number (or non-representative set) of level-1 observations for levels-2 or 3.
  • For a more detailed application of multilevel logistic modelling, study Sommet & Morselli (2017): Keep Calm and Learn Multilevel Logistic Modeling: A Simplified Three-Step Procedure Using Stata, R, Mplus, and SPSS, International Review of Social Psychology, 30(1), 203-218.
  • For an application in the field of (Economic) Geography, study Srholec (2010): A Multilevel Approach to Geography of Innovation, Regional Studies, 44(9), 1207-1220.

Methods for Analyzing Limited Dependent Variables and Endogeneity

  • Limited dependent variables can only take the value of 0 or 1, and are often used in models to predict binary outcomes.
  • Linear regression models can be used to analyze limited dependent variables, but may not be the most appropriate method.
  • Binomial regression and logistic regression are alternative methods for analyzing limited dependent variables, and can provide more accurate predictions.
  • Logistic regression analyzes the relationship between an independent variable and the natural log of the odds ratio for the dependent variable.
  • The odds ratio represents the likelihood of an event occurring, and can be used to compare the probability of the dependent variable taking on one value versus another.
  • Correlated missing variables and sample selection can impact the accuracy of regression models, and should be taken into account when analyzing limited dependent variables.
  • Endogeneity occurs when a variable of interest is impacted by other variables in the model, and can lead to inaccurate results.
  • Instrumental variables (IV) can be used to address endogeneity, by finding an independent variable that is correlated with the variable of interest but not with the error term.
  • Two-stage least squares (2SLS) is a commonly used method for analyzing endogeneity with IV.
  • Regression models can be evaluated using various statistical tests, including joint sign F-tests, likelihood-ratio tests, and Hosmer and Lemeshow tests.
  • Interpretation of regression models should focus on the change in one independent variable, while holding all other variables constant.
  • Polynomial regression models can be used to analyze relationships that are not linear, by including higher order terms in the model.

Methods for Analyzing Limited Dependent Variables and Endogeneity

  • Limited dependent variables can only take the value of 0 or 1, and are often used in models to predict binary outcomes.
  • Linear regression models can be used to analyze limited dependent variables, but may not be the most appropriate method.
  • Binomial regression and logistic regression are alternative methods for analyzing limited dependent variables, and can provide more accurate predictions.
  • Logistic regression analyzes the relationship between an independent variable and the natural log of the odds ratio for the dependent variable.
  • The odds ratio represents the likelihood of an event occurring, and can be used to compare the probability of the dependent variable taking on one value versus another.
  • Correlated missing variables and sample selection can impact the accuracy of regression models, and should be taken into account when analyzing limited dependent variables.
  • Endogeneity occurs when a variable of interest is impacted by other variables in the model, and can lead to inaccurate results.
  • Instrumental variables (IV) can be used to address endogeneity, by finding an independent variable that is correlated with the variable of interest but not with the error term.
  • Two-stage least squares (2SLS) is a commonly used method for analyzing endogeneity with IV.
  • Regression models can be evaluated using various statistical tests, including joint sign F-tests, likelihood-ratio tests, and Hosmer and Lemeshow tests.
  • Interpretation of regression models should focus on the change in one independent variable, while holding all other variables constant.
  • Polynomial regression models can be used to analyze relationships that are not linear, by including higher order terms in the model.

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Advanced Statistical Analysis Lecture 10

Description

p, odds, ln(odds) calculations, model fit statistics, violating the assumption of homoskedastic errors, endogeneity and 2SLS, instrumental variable approach and the multinomial logistic regression

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