DATA TYPES AND MEASUREMENT ERROR Four types of

DATA TYPES AND MEASUREMENT ERROR • Four types of variables in the V-Dem Dataset • A and B variables • free – we assume – from Measurement Error 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 1

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DATA TYPES AND MEASUREMENT ERROR • Four types of variables in the V-Dem Dataset • A and B variables • free – we assume – from Measurement Error • C variables • Measurement Model C Variables • V-Dem Measurement Model aggregates coders’ scores using a Bayesian IRT Model. Posteriors estimated by the MM 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 3

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DATA TYPES AND MEASUREMENT ERROR • Four types of variables in the V-Dem Dataset • A and B variables • free – we assume – from Measurement Error • C variables • Measurement Model C Variables • V-Dem Measurement Model aggregates coders’ scores using a Bayesian IRT Model. Posteriors estimated by the MM • Bootstrap C Variables • Bootstrap procedure to aggregate coders’ scores. Usually % variables 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 5

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DATA TYPES AND MEASUREMENT ERROR • Four types of variables in the V-Dem Dataset • A and B variables • free – we assume – from Measurement Error • C variables • Measurement Model C Variables • V-Dem Measurement Model aggregates coders’ scores using a Bayesian IRT Model. Posteriors estimated by the MM • Bootstrap C Variables • Bootstrap procedure to aggregate coders’ scores. Usually % variables • D Variables (Indices) • Aggregation of 2+ A, B, or C variables using Bayesian Factor Analysi (BFA). Posteriors of the BFA are the uncertainty estimates 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 7

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EXAMPLES • In this tutorial, • we explain how to incorporate uncertainty estimates for Measurement Model C variables and for Indices (D variables). • A and B variables should be treated as error free • and Bootstrap C Variables depend on a more complex estimation strategy that we will not cover. 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 9

BEFORE WE START • Find the Box Folder I shared with you this morning; • There you have copies of the dataset (Stata 13 and Stata 14 copies!) and all the do-files. • Do-Files were prepared using Stata 14, but we do not anticipate any conflict if you are using Stata 13. • Go to https: //curate. nd. edu • Search for “Posteriors” 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 10

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DOWNLOADING THE POSTERIORS • In the examples today we will use: • Freedom of Discussion for Women • Civil Liberties -> v 2 cldiscw • Clean Elections • Indices -> frefair • Freedom of Association • Indices -> frassoc_thick • Freedom of Expression • Indices -> freexp_thick 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 13

DOWNLOADING THE POSTERIORS • If you downloaded the files for a Measurement Model C variable (in this case, v 2 cldiscw): • You have a file with 5. csv files Table 1. Description of the matrices created by the V-Dem Measurement Model Matrix Description Z Uncertainty Estimates. Posteriors B Rater discrimination parameters Gamma Rater thresholds Gamma c Hierarchical parameter. Average threshold of raters within countries Gamma u Sample averages • If you downloaded an Index: • You have 1 one. csv file. The Posterior distribution of the BFA • Unzip the files and save the matrices in some folder you can easily access 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 14

EXAMPLE A • DV: Infant Mortality Rate • IV: Freedom of discussion for women • Control: GDP per capita (logged) • Model: fixed effects regression, clustered standard errors (by country) • Codes are in the “Example. A. do” in the Box Folder 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 15

EXAMPLE B • DV: Infant Mortality Rate • IV: Clean Elections Index • Control: GDP per capita (logged) • Model: fixed effects regression, clustered standard errors (by country) • Codes are in the “Example. B. do” in the Box Folder 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 16

EXAMPLE C • DV: Infant Mortality Rate • IV: Freedom of discussion for women AND Clean Elections Index • Control: GDP per capita (logged) • Model: fixed effects regression, clustered standard errors (by country) • Codes are in the “Example. C. do” in the Box Folder 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 17

EXAMPLE D • DV: Infant Mortality Rate • IV: Multiplicative Electoral Democracy Index (MEDI) [Gerring et al. 2016] • Control: GDP per capita (logged) • Model: fixed effects regression, clustered standard errors (by country) • Codes are in the “Example. D. do” in the Box Folder 3/18/2016 Varieties of Democracy Data: Incorporating Measurement Error 18