47 Questions
What is another name for multilevel modelling?
Mixed model
What is the variance partition coefficient (VPC) or intraclass correlation coefficient (ICC)?
A measure of the variation between higher level units
When is multilevel modelling not appropriate?
When there is no significant variation of the intercept
What is the main advantage of fixed effects models?
They remove all variation between higher level units from parameter estimation
What is the minimum VPC/ICC value that should not be ignored when analyzing hierarchical data?
5%
What are some examples of multilevel modelling settings?
All of the above
What is the main assumption of multilevel analysis for making causal inferences?
Random allocation of people within the different higher unit levels
What is the main drawback of fixed effects models?
They estimate time-invariant variables on the higher level units
What type of regression models can be extended to multilevel models?
All regression models can be extended to multilevel models
When is multilevel modelling appropriate?
When interested in interaction effects of variables on different levels
What is the main difference between linear regression model with one level and multilevel regression model with two levels?
The number of levels included in the model
What is endogeneity in regression models?
The pollution of the coefficient of the variable of interest
What are instrumental variables?
Variables that are uncorrelated with the variable of interest and the error term
What are the properties of valid instruments?
cov(H, ϵ) ̸= 0 and cov(H, x) = 0
What is the 2-Stage Least Squares (2SLS) method used for?
To avoid reverse causality in a regression model
What is the first step in the 2SLS method?
Regress the endogenous variable on the instrument
What is the second step in the 2SLS method?
Predict the value of the endogenous variable given the values of the instrument
What is the logistic regression equation used for?
To model the probability of a binary outcome
What is the interpretation of the coefficient in the logistic regression equation?
If x increases with 1 unit, ln(odds) increases with b1
What is the formula for interpretation polynomials used for?
To interpret the effect of a variable on the dependent variable
What is the interpretation of the slope in the formula for interpretation polynomials?
A linear line increasing in x if b2 is positive
What is the null hypothesis in the Likelihood-Ratio test for logistic regression?
The model with constant only is a better fitting model
What is the Hosmer and Lemeshow test used for in logistic regression?
To test the goodness-of-fit of the logistic regression model
What is the main issue with correlated missing variables in statistical analysis?
It can lead to biased estimates and incorrect conclusions
What is the main issue with sample selection in statistical analysis?
It narrows the interpretation of results to a specific group within the population
What is reverse causality in statistical analysis?
When the independent variable is causing the outcome variable
What are instrumental variables in statistical analysis?
Variables that are correlated with the independent variable but uncorrelated with the error term
What are the properties of valid instruments in statistical analysis?
cov(H, ϵ) = 0 and cov(H, x) ̸= 0
What is the 2-Stage Least Squares (2SLS) method in statistical analysis?
A method for linear regression models with multiple independent variables
What is the main advantage of the 2-Stage Least Squares (2SLS) method in statistical analysis?
It is not affected by endogeneity
What is the Joint sign F-test in linear regression models?
A test for the overall significance of the model
What is the Maximum likelihood method in logistic regression?
A method for estimating the coefficients of the logistic regression equation
What is the Likelihood-Ratio test in logistic regression?
A test for the goodness of fit of the model
What is the main advantage of the Hosmer and Lemeshow test in logistic regression?
It tests the goodness of fit of the model
What is the formula for interpretation polynomials in statistical analysis?
y = b0 + b1x + b2x^2
Linear regression models can be used to analyze the relationship ______ independent and dependent variables
between
Logistic regression models are used when the dependent variable is ______ (0 or 1)
binary
Sample selection and correlated missing variables can impact the ______ of regression results
interpretation
Endogeneity can occur when the independent variable is affected by the ______ term
error
2-Stage Least Squares (2SLS) is a method for using ______ variables to address endogeneity
instrumental
OLS joint sign F-test and R-squared values can be used to evaluate the ______ of linear regression models
fit
Maximum likelihood and likelihood ratio tests can be used to evaluate the ______ of logistic regression models
fit
Pseudo R-squared values and the Hosmer and Lemeshow test can also be used to evaluate the ______ of logistic regression models
fit
The interpretation of coefficients in regression models depends on the type of model and the specific ______ included
variables
In linear regression models, the interpretation is based on the change in the dependent variable for a ______-unit increase in the independent variable
one
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
odds
Polynomial regression models can be used to analyze ______ relationships between variables
non-linear
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.
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
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
