Game-changers: . Detecting shifts in the flow of campaign - PowerPoint PPT Presentation

. Game-changers: . Detecting shifts in the flow of campaign contributions . University of Rochester . Matthew Blackwell . APWG . March 8th, 2013

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. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.

. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.

. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.

. Why not polls? . Lack of variation . 1. . Cheap talk . 2. . Data (un)availability . 3.

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When do campaign contributions take off or fall flat? . A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data.

. A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data. When do campaign contributions take off or fall flat?

. A measurement question . When do campaigns take off or fall flat? . . Tools: Bayesian nonparametric model for overdispersed count data. When do campaign contributions take off or fall flat?

. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.

. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.

. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.

. Why contributions? . Lots of variation . 1. . Costly participation . 2. . Data availability . 3.

. 0 . 2000 . 1500 . 1000 . 500 . . . 200 . 150 . 100 . 50 . 0 . Why changepoint models?

. The challenges . Modeling daily contribution counts . Choosing the number of changepoints

. The challenges . Modeling daily contribution counts . Choosing the number of changepoints

. 0 . 2500 . 2000 . 1500 . 1000 . 500 . . . Jan 12 . Oct 11 . Jul 11 . Apr 11 . Contributions . Number of . Overdispersion in campaign contributions

𝜇 𝑢 = exp (𝑌 𝑢 𝛾) . (link function) . [𝑧 𝑢 |𝛾, 𝜍, 𝑌] ∼ NegBin (𝜍, 𝜍/(𝜍 + 𝜇 𝑢 )) . (random effect) . [𝜃 𝑢 |𝜍] ∼ Gamma (𝜍, 𝜍) . . Bayesian model for overdispersed counts . (data) . [𝑧 𝑢 |𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . For observations 𝑢 in {1, … , 𝑈} : . marginal distribution of 𝑧 :

. (link function) . [𝑧 𝑢 |𝛾, 𝜍, 𝑌] ∼ NegBin (𝜍, 𝜍/(𝜍 + 𝜇 𝑢 )) . (random effect) . [𝜃 𝑢 |𝜍] ∼ Gamma (𝜍, 𝜍) . . Bayesian model for overdispersed counts . (data) . [𝑧 𝑢 |𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . For observations 𝑢 in {1, … , 𝑈} : . marginal distribution of 𝑧 : 𝜇 𝑢 = exp (𝑌 𝑢 𝛾)

. (link function) . [𝑧 𝑢 |𝛾, 𝜍, 𝑌] ∼ NegBin (𝜍, 𝜍/(𝜍 + 𝜇 𝑢 )) . (random effect) . [𝜃 𝑢 |𝜍] ∼ Gamma (𝜍, 𝜍) . . Bayesian model for overdispersed counts . (data) . [𝑧 𝑢 |𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . For observations 𝑢 in {1, … , 𝑈} : . marginal distribution of 𝑧 : 𝜇 𝑢 = exp (𝑌 𝑢 𝛾)

. (link function) . [𝑧 𝑢 |𝛾, 𝜍, 𝑌] ∼ NegBin (𝜍, 𝜍/(𝜍 + 𝜇 𝑢 )) . (random effect) . [𝜃 𝑢 |𝜍] ∼ Gamma (𝜍, 𝜍) . . Bayesian model for overdispersed counts . (data) . [𝑧 𝑢 |𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . For observations 𝑢 in {1, … , 𝑈} : . marginal distribution of 𝑧 : 𝜇 𝑢 = exp (𝑌 𝑢 𝛾)

𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . . . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . (link function) Generalize to a mixture model . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} )

𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . (link function) . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . . Generalize to a mixture model . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝑡 𝑢 = 𝑙

Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . (link function) . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . . Generalize to a mixture model . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙

Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . (link function) . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . . Generalize to a mixture model . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙

Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . Generalize to a mixture model . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . (link function) . . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙

Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0 . Generalize to a mixture model . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . (link function) . . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙

. Generalize to a mixture model . . . . (random effect) . [𝜃 𝑢 |𝜍, 𝑡 𝑢 ] ∼ Gamma (𝜍 𝑙 , 𝜍 𝑙 ) . (link function) . . (1, … , 𝐿) . regimes . . (data) . [𝑧 𝑢 |𝑡 𝑢 , 𝜃 𝑢 , 𝛾, 𝜍, 𝑌] ∼ Poisson (𝜃 𝑢 𝜇 𝑢 ) . ( ∀𝑘 ∉ {𝑙, 𝑙 + 1} ) 𝜇 𝑢 = exp (𝑌 𝑢 𝛾 𝑙 ) 𝑡 𝑢 = 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 | 𝑡 𝑢 = 𝑙) = 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑙 + 1 | 𝑡 𝑢 = 𝑙) = 1 − 𝑞 𝑙 Pr(𝑡 𝑢+􏷡 = 𝑘 | 𝑡 𝑢 = 𝑙) = 0

. 𝑞 􏷡 . 1 . 2 . 3 . . . 1 − 𝑞 􏷡 . changepoint . ⋯ . N . Units (𝛾 􏷤 , 𝜍 􏷤 ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (𝛾 􏷡 , 𝜍 􏷡 ) . Regimes . (𝛾 􏷢 , 𝜍 􏷢 ) . (𝛾 􏷣 , 𝜍 􏷣 ) Must be in the last regime

. 𝑞 􏷡 . 1 . 2 . 3 . . . 1 − 𝑞 􏷡 . changepoint . ⋯ . N . Units (𝛾 􏷤 , 𝜍 􏷤 ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (𝛾 􏷡 , 𝜍 􏷡 ) . Regimes . (𝛾 􏷢 , 𝜍 􏷢 ) . (𝛾 􏷣 , 𝜍 􏷣 ) Must be in the last regime

. 𝑞 􏷡 . 1 . 2 . 3 . . . 1 − 𝑞 􏷡 . changepoint . ⋯ . N . Units (𝛾 􏷤 , 𝜍 􏷤 ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (𝛾 􏷡 , 𝜍 􏷡 ) . Regimes . (𝛾 􏷢 , 𝜍 􏷢 ) . (𝛾 􏷣 , 𝜍 􏷣 ) Must be in the last regime

. 𝑞 􏷡 . 1 . 2 . 3 . . . 1 − 𝑞 􏷡 . changepoint . ⋯ . N . Units (𝛾 􏷤 , 𝜍 􏷤 ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (𝛾 􏷡 , 𝜍 􏷡 ) . Regimes . (𝛾 􏷢 , 𝜍 􏷢 ) . (𝛾 􏷣 , 𝜍 􏷣 ) Must be in the last regime

. 𝑞 􏷡 . 1 . 2 . 3 . . . 1 − 𝑞 􏷡 . changepoint . ⋯ . N . Units (𝛾 􏷤 , 𝜍 􏷤 ) Traditional changepoint models . . 1 . Regimes . 2 . 3 4 . . (𝛾 􏷡 , 𝜍 􏷡 ) . Regimes . (𝛾 􏷢 , 𝜍 􏷢 ) . (𝛾 􏷣 , 𝜍 􏷣 ) Must be in the last regime