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Supplementary Appendix for “Mind the Gap”
Table A. Names and Wording for Political Knowledge Items
Label / Wording / Response optionsi. Instruction Prompt / Now we are going to ask you a few questions about the government in Washington, D.C. Many people do not know the answers to these questions, but please do the best that you can to answer each one without any help from another source (for example, an internet search or asking someone else).
1) Conservative party*
*Version a) or b) randomly assigned. / a) In general, thinking about the political parties in Washington, would you say Democrats are more conservative than Republicans, or Republicans are more conservative than Democrats?
b) In general, thinking about the political parties in Washington, would you say Republicans are more conservative than Democrats, or Democrats are more conservative than Republicans? / 1) Democrats are more conservative than Republicans
2) Republicans are more conservative than Democrats
3) I don’t know
1) Republicans are more conservative than Democrats
2) Democrats are more conservative than Republicans
3) I don’t know
2) Constitutional law / Whose responsibility is it to determine if a law is constitutional or not? / 1) the President
2) Congress
3) the Supreme Court
4) I don’t know
3) Veto override / How much of a majority is required for the U.S. Senate and House to override a presidential veto? / 1) one half plus one vote
2) three-fifths
3) two-thirds
4) three quarters
5) I don’t know
4) John Roberts / What job or office is now held by John Roberts? / 1) Secretary of the Treasury Department
2) Vice-President of the United States
3) Chief Justice of the U.S. Supreme Court
4) I don’t know
5) John Boehner / What job or political office does John Boehner now hold? / 1) Vice-President of the United States
2) Speaker of the U.S. House of Representatives
3) U.S. Ambassador to China
4) I don’t know
6) Stay of deportation / In June 2012, it was announced that illegal immigrants who came to the U.S. under the age of 16 would be able to live and work here for two years if they met various requirements, including a clean criminal record. What government institution was formally responsible for this policy change? / 1) The U.S. Supreme Court
2) The U.S. Congress
3) The Office of the President of the United States
4) I don’t know
7) Sonia Sotomayor / What job or office does Sonia Sotomayor now hold? / 1) Secretary of Homeland Security
2) News reporter for Univision News
3) Justice of the U.S. Supreme Court
4) I don’t know
8) Marco Rubio / What job or office does Marco Rubio now hold? / 1) News reporter for Telemundo News
2) Secretary of Health and Human Services
3) U.S. Senator
4) I don’t know
Section B. Technical Details ofthe Confirmatory Factor Analysisof my Binary Items
I use confirmatory factor analysis (CFA) to test the performance of my eight (8) binary factual questions. Psychometric work shows that CFAs of binary items like mine are equivalent to two-parameter Item Response Theory (IRT) models (cf. Glöckner-Rist and Hoijtink 2003; Moustaki et al. 2003), where the two parameters are the item loadings (discrimination) and thresholds (difficulties). The one-factor CFA model I estimate is specified by the following equation:
xm = λm ξ + δm (Eq. 1)
where (ξ) is latent political knowledge, (xm)is an observed factual item tapping this trait, (λm) is the loading relating latent knowledge to an observed item, and (δm) is a random error term. This general model assumes the response variable (x*) underlying each observed item is continuous: x = x*. But my items are binary, so x ≠ x*. Equation 1 is thus modified in two ways.
First, since x* is theoretically continuous, the relation between ξ and x* is estimated rather than the relation between ξ and x (Finney and DiStefano 2006). Hence, the resulting loadings (λm) capture the relation between latent knowledge and the response variable underlying an observed factual question, thus providing that sense of how well an item discriminates between people with varied knowledge levels (figure 1).
Second, item thresholds (τ) are estimated. Each item has c – 1 thresholds, where c = the number of item categories. Here thresholds are values on a latent response variable (xm*) that move a person from an incorrect to correct response on an observed factual question (xm), thus telling us how difficult an item is to answer (figure 1). Since latent response variables have no intrinsic metric, their mean and standard deviation are set to (0, 1), making thresholds nothing more than z-values.
Table C. CFA Results for Political Knowledge Items – Latinos and Whites
Item / Item Loadings &Thresholds(Latinos) / Item Loadings &
Thresholds (Whites)
1. Conservative party / .591/(.047)
-.077 / .657/(.048)
-.834
2. Constitutional law / .724/(.039)
-.077 / .734/(.047)
-.947
3. Veto override / .601/(.050)
.573 / .463/(.052)
-.298
4. John Roberts / .831/(.032)
.454 / .870/(.026)
-.270
5. John Boehner / .851/(.028)
.127 / .920/(.028)
-.840
6. Stay of deportation / .529/(.051)
.279 / .554/(.048)
.106
7. Sonia Sotomayor / .680/(.046)
-.499 / .862/(.027)
-.379
8. Marco Rubio / .738/(.037)
-.017 / .800/(.031)
-.110
N / 505 / 559
RMSEA [90% CI] / .068/[.055, .080] / ---
CFI / .976 / ---
TLI / .967 / ---
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Table D. General Versus Domain-Specific Models of Political Knowledge Among Latinos and Whites
Knowledge:General
(Latinos) / Knowledge:
Domain-Specific
(Latinos) / Knowledge:
General
(Whites) / Knowledge:
Domain-Specific
(Whites)
# of eigenvalues > 1.00/ observed value / 1/
4.30 / 1/
4.30 / 1/
4.80 / 1/
4.80
# of estimated factors / 1 / 2 / 1 / 2
Inter-factor correlation / --- / .80 / --- / .97
RMSEA [90% CI] / .068 [.055, .080] / .056 [.038, .074] / .068 [.055, .080] / .049 [.030, .068]
CFI / .976 / .978 / .976 / .990
TLI / .967 / .972 / .967 / .985
Table E. Transformation of CFA Loadings and Thresholds to IRT Discrimination and Difficulty Parameters
[1] CFA Loadings/Thresholds (Latinos) / [2] IRT Discriminations/Difficulties(Latinos) / [3] CFA Loadings/Thresholds (Whites) / [4] IRT Discriminations/Difficulties
(Whites)
Conservative party / .591/
-.077 / .732/
-.130 / .657/
-.834 / .871/
-1.270
Constitutional law / .724/
-.077 / 1.050/
-.106 / .734/
-.947 / 1.080/
-1.291
Veto override / .601/
.573 / .753/
.953 / .463/
-.298 / .523/
-.643
John Roberts / .831/
.454 / 1.497/
.547 / .870/
-.270 / 1.760/
-.311
John Boehner / .851/
.127 / 1.621/
.149 / .920/
-.840 / 2.350/
-.913
Stay of deportation / .529/
.279 / .623/
.528 / .554/
.106 / .665/
.191
Sonia Sotomayor / .680/
-.499 / .926/
-.734 / .862/
-.379 / 1.704/
-.439
Marco Rubio / .738/
-.017 / 1.095/
-.024 / .800/
-.11 / 1.333/
-.138
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TableF. Percent DKs by Item and Group Under Analysis
A.Un-harmonized items / Constitutional law / Vetooverride / John
Roberts / John Boehner / Mean DK
Latinos (L) / 14% / 37% / 54% / 46% / 38%
Whites (W) / 7% / 20% / 30% / 17% / 19%
Mean DK Gap (L - W) / --- / --- / --- / --- / -19%
B. Harmonized items / Conservative
party / Stay of deportation / Sonia Sotomayor / Marco
Rubio / Mean DK
Latinos (L) / 29% / 29% / 26% / 44% / 32%
Whites (W) / 11% / 30% / 28% / 35% / 26%
Mean DK Gap (L - W) / --- / --- / --- / --- / -6%
Table G. Invariance Tests of Knowledge Items
Unrestricted model / Conservative party / Constitutionlaw / Veto override / John
Roberts / John Boehner / Stay of deportation / Sonia Sotomayor / Marco Rubio
RMSEA
[90% CI] / .068
[.055, .080] / .092
[.080, .104] / .102
[.091, .114] / .107
[.095, .119] / .100
[.089, .112] / .113
[.102, .125] / .068
[.056, .081] / .069
[.057, .081] / .066
[.054, .079]
CFI / .976 / .955 / .944 / .939 / .947 / .932 / .975 / .975 / .977
TLI / .967 / .939 / .924 / .917 / .927 / .907 / .966 / .965 / .968
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Table H. Decreased Scale Reliability Does Not Substantially Alter the Variability of the Null Association Between Latino Status and Political Knowledge
4-item scale, α = .62 / 3-item scale, α = .49(Marco Rubio) / 3-item scale, α = .49
(Sonia Sotomayor) / 3-item scale, α = .57
(Stay of Deportation)
Latino / .034
[-.005, .074] / .007
[-.035, .049] / .027
[-.015, .068] / .027
[-.016, .070]
Adj. R2 / .29 / .27 / .26 / .28
N / 974 / 974 / 974 / 974
While it would be ideal to add one more unbiased item to this scale to test whether enhanced reliability allows a
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Table I. Residence in States With High Latino Populations is Unassociated With Knowledge Levels on the Harmonized Scale
Political Knowledge (1) / Political Knowledge (2) / Political Knowledge (3) / Political Knowledge (4)Florida / --- / .05 (.04) / --- / ---
New York / --- / .03 (.04) / --- / ---
California / --- / .00 (.03) / --- / ---
Texas / --- / .04 (.03) / --- / ---
Illinois / --- / .00 (.05) / --- / ---
All Latino states / --- / --- / .02 (.02) / .05^ (.03)
Latino / .03 (.02) / .03 (.03) / .03 (.03) / .05^ (.03)
All Latino states x Latino / --- / --- / --- / -.06 (.04)
Income / .19* (.04) / .19* (.04) / .19* (.04) / .19* (.04)
Education / .20* (.03) / .20* (.03) / .20* (.03) / .20* (.03)
Age / .24* (.04) / .23* (.04) / .24* (.04) / .24* (.04)
Female / -.04* (.02) / -.04* (.02) / -.04* (.02) / -.04 (.02)
Political Interest / .31* (.03) / .31* (.03) / .31* (.03) / .31* (.03)
Political Efficacy / .08* (.03) / .08* (.03) / .08* (.03) / .08* (.03)
Second generation / -.07^ (.04) / -.07^ (.04) / -.07^ (.04) / -.07^ (.04)
Third generation / -.07^ (.04) / -.07^ (.04) / -.07^ (.04) / -.07^ (.04)
U.S. citizen / .04 (.04) / .04 (.04) / .04 (.04) / .04 (.04)
Spanish interview / .07^ (.04) / .07^ (.04) / .
07^ (.04) / .07^ (.04)
Constant / .08 (.05) / .08 (.05) / .08 (.05) / .07 (.05)
Adj. R2 / .29 / .29 / .29 / .29
N / 974 / 974 / 974 / 974
Table J. Support for Stricter Illegal Immigration Policy by Knowledge Levels Among Latinos and Whites
1. Illegal Immigration Policy(Citizenship) / 2. Illegal Immigration Policy
(Citizenship)
Political Knowledge / -.50* (.17)a / -.37* (.15)b
Latino / -1.13* (.17) / -.65* (.15)
Knowledge x Latino / .73* (.23) / -.00 (.22)
Partisanship (Democrat) / -.08* (.02) / -.08* (.02)
Ideology / .60* (.19) / .53* (.19)
Education / -.22^ (.12) / -.14 (.12)
Age / .10 (.17) / .22 (.18)
Female / -.17* (.07) / -.21* (.07)
Marital Status / -.14^ (.07) / -.15* (.07)
Employment status / .02 (.08) / .03 (.08)
Border state / -.08 (.08) / -.10 (.08)
Cut point-1 / -1.74* (.23) / -1.57* (.22)
Cut point-2 / -.81* (.23) / -.63* (.22)
Cut point-3 / -.09* (.23) / .09 (.22)
LnL / -1300.57 / -1300.97
Χ2 / 191.17* / 194.66*
N / 1020 / 1020
Table K. Obama FT Ratings Among Latino and White Democrats by Knowledge Levels
1. Obama FT Rating / 2. Obama FT RatingPartisanship (Democrat) / 8.92* (1.30) / 7.69* (1.00)
Political Knowledge / .54 (6.98) a / -8.59 (5.73) b
Latino / 42.63* (8.51) / 28.29* (8.18)
Partisanship x Knowledge / .63 (1.61) / 2.67* (1.31)
Partisanship x Latino / -5.36* (1.80) / -3.59* (1.72)
Knowledge x Latino / -45.21* (11.09) / -18.66^ (11.19)
Partisan. x Know. x Latino / 7.00* (2.40) / 3.46 (2.36)
Ideology / -25.20* (3.91) / -24.05* (3.86)
Racial resentment / -10.88* (3.44) / -11.86* (3.45)
Age / 4.49 (3.56) / 3.18 (3.59)
Education / .17 (2.58) / -2.04 (2.42)
Female / 1.61 (1.44) / 2.36^ (1.43)
Marital status / 1.64 (1.54) / 2.30 (1.55)
Employment status / 1.07 (1.56) / .67 (1.57)
Southern state / .12 (1.48) / .13 (1.49)
Constant / 23.30* (6.93) / 30.92 (5.97)
R2 / .59 / .58
N / 977 / 977
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Figure L. Marginal Effect of Democrat PID on Obama Favorability Rating by Knowledge Level Among Latinos and Whites (with 95% confidence intervals)
Section M. Explanation and Discussion of Results in Table K and Figure L (i.e., Obama Analysis)
I further demonstrate that uneven item performance affects inferences regarding knowledge’s influence on political judgments by examining how greater political information facilitates judgments that are more consistent with people’s underlying political predispositions (Zaller 1992; Bartels 1996; Althaus 1998). Specifically, I investigateevaluations of President Obama among self-identified partisans with varied knowledge levels. Insofar as greater knowledge forges stronger links between people’s predispositions and political judgments, one would expect self-identified Democrats with higher knowledge levels to rate their co-partisan—President Obama—more favorably than self-identified Republicans. That is, political knowledge should assist people in drawing stronger connections between their partisan allegiance and evaluation of the president (e.g, Delli Carpini and Keeter 1996; Zaller 1992). And, since partisanship cuts across race/ethnicity, this pattern should similarly emerge among Latinos and Whites.
Thus, I regressed feeling thermometer ratings of President Obama on individual differences in partisanship, political knowledge, Latino status, and the relevant interactions between these three variables, plus controls for ideology, racial resentment, age, education, gender, marital status, employment status, and Southern residence.[1]Given my discussion above, we should observe two patterns. First, as individual knowledge levels increase, the association between Democratic self-identification and favorable Obama ratings should strengthen. Second, this general pattern should emerge in parallel among both Latinos and Whites. Table K(SA) reports the raw results.
Panel A (figure L, SA) shows that with the un-harmonized knowledge scale, the expected pattern holds for Latinos, but not Whites. For Whites, the association between Democratic partisanship and Obama’s favorability rating is unrelated to knowledge, as evidenced by the solid flat line. Among Whites with the lowest knowledge level, stronger Democratic partisanship is associated with an 8.92 [95% CI: 6.37, 11.47] increase in Obama’s rating, while among Whites with the highest knowledge level, stronger Democratic partisanship increases this rating by 9.55 [95% CI: 8.16, 10.94]—a small and unreliable shift. This contradicts prior work, which expects a reliable and positive association between knowledge levels, partisanship, and presidential ratings (Delli Carpini and Keeter 1996; Zaller 1992). Peculiarly, Latinos do display the expected pattern. Among Latinos with the lowest political knowledge level, stronger Democratic partisanship yields a favorability increase of 3.56 [95% CI: 1.08, 6.05], while among Latinos with the highest information levels, this rating climbs significantly by 11.19 [95% CI: 9.20, 13.18]. Hence, the un-harmonized scale detects the expected theoretical pattern only among Latinos.
In contrast, both Latinos and Whites display the expected relationship with the harmonized scale, with higher knowledge levels strengthening the association between Democratic partisanship and evaluations of President Obama among members of both groups. In fact, the pattern is statistically indistinguishable between both groups. This appears to result from the harmonized scale’s better performance among Whites with low levels of political knowledge. Among Whites with the lowest knowledge level, stronger Democratic partisanship is associated with an increase of 7.69 [95% CI: 5.73, 9.65] in Obama’s rating. But among Whites with the highest knowledge level, Obama’s rating now rises by 10.36 [95% CI: 8.92, 11.79]—an increase just shy of significance at the 10% level.[2] In turn, Obama’s favorability rating jumps by 4.10 [95% CI: 1.29, 6.91] among Latinos who strongly identify as Democrats and display low knowledge, which is statistically similar to the shift among Whites with the same level of partisanship and knowledge. This rating increases significantly by 10.22 [95% CI: 8.30, 12.14] among Latinos who strongly identify as Democrats and have high knowledge, a shift that is, again, statistically identical to the one among Whites with the same level of partisanship and knowledge. Thus, the harmonized knowledge scale more reliably detects the anticipated theoretical relation among both Latinos and Whites. And, it appears to do so because it operates equivalently across these groups.
[1]This model closely parallels those in Piston (2010), who analyzed thermometer ratings of Democratic figures. Save for Obama’s feeling thermometer ratings (which run from 0-100) and partisanship (which runs from 1 to 7), all variables run on a 0-1 interval. See table K (SA) for details on coding of covariates.
[2]The corresponding estimates are: 7.69 [90% CI: 6.05, 9.34] and 10.36 [90% CI: 9.15, 11.56].