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

    What are some examples of multilevel modelling settings?

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

    When is multilevel modelling appropriate?

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

    What is endogeneity in regression models?

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

    What are the properties of valid instruments?

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

    What is the first step in the 2SLS method?

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

    What is the logistic regression equation used for?

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

    What is reverse causality in statistical analysis?

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

    What is the formula for interpretation polynomials in statistical analysis?

    <p>y = b0 + b1x + b2x^2</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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