Enseñanza de la física

Table 2.2 presents multilevel models of retrospective national economic evaluation. I run one random intercept model (model 1) and five random slope models (models 2 through 6). The interpretation of the six multilevel models is as follows. 2.2.1 Random Intercept Model

Model 1 is a random intercept model, which allows the model intercept to vary randomly across countries. For fixed effects coefficients, retrospective and prospective pocketbook evaluation, media consumption, and talking about politics with others are individually significant. When respondents positively evaluated their past and future personal economic evaluation, they were more likely to believe national economic condition had become better over the past year. The more time they spent watching

television, the more negatively they tended to view retrospective national economic condition.

Figure 1 presents the effects of media consumption on retrospective national economic evaluation by each country on fixed effect. The figure shows that more media consumption does not increase the probability of positive retrospective national economic condition. In contrast to media consumption, talking more about politics with others leads to positive retrospective national economic evaluation. The intercept variance is 0.291. The likelihood ratio statistic with a corresponding p-value of .000 indicates that there is between-country variance across countries. In other words, the variation of retrospective national economic evaluation can be attributed to between-country factors.

2.2.2 Random Slope Models (Models 2 thorough 6)

The random intercept model in model 1 shows significant between-country variance in retrospective national economic evaluation. Models 2 through 6 are random slope models, which allow the effects of level of democracy (polity score) and level of economic development (GDP per capita) to vary across nations. Models 3 and 5 allow the random intercepts and slopes to co-vary (as opposed to the default, in which they are uncorrelated).

2.2.2.1 Random Coefficients of Polity Score (Models 2 and 3)

Model 2 is a random slope model that allows polity score to vary across countries. There is no difference in the fixed effects coefficients and standard errors in models 1 and 2. In model 2, the intercept variance is the same as in model 1, and the random coefficient of polity score is close to zero. Apparently, polity score does not explain much of the

variance across countries. In other words, level of democracy in general may have little influence on retrospective national economic evaluation.

Model 3 is a random slope model with correlated variance. Most of the fixed effects coefficients are the same as those in model 2. The coefficients of prospective pocketbook evaluation and political sophistication change slightly, but only prospective pocketbook evaluation is individually significant. The between-country variance as a function of polity score is as follows:

var(𝑢_0𝑗+ 𝑢_8𝑗𝑝𝑜𝑙𝑖𝑡𝑦_𝑖𝑗) = var(𝑢_0𝑗) + 2cov(𝑢_0𝑗𝑢_8𝑗)𝑝𝑜𝑙𝑖𝑡𝑦_𝑖𝑗+ var(𝑢_8𝑗)𝑝𝑜𝑙𝑖𝑡𝑦_𝑖𝑗2

= 0.024 − 0.10 𝑝𝑜𝑙𝑖𝑡𝑦_𝑖𝑗 + 0.09 𝑝𝑜𝑙𝑖𝑡𝑦_𝑖𝑗2

Figure 2.2 shows the graph of the between-country variance as a function of polity score. The between-country variance increases rapidly as a function of polity score. The likelihood ratio test can determine whether polity score can explain any of the

between-country variance of the effect of information sources on retrospective national economic evaluation. The likelihood ratio test (assuming the uncorrelated equation model 2 is nested within the correlated equation model 3) is not significant (p = 1.000 > .05). It implies that the correlated variance model (model 3) is not necessarily more appropriate than the uncorrelated variance model (model 2). Moreover, the likelihood ratio test (assuming the restricted equation model 1 is nested within the unrestricted equation model 3) is also not significant (p = 1.000 > .05). The two likelihood ratio tests confirm that the random effect for polity score is not significant and does not account much for between-country variance of retrospective national economic evaluation.

2.2.2.2 Random Coefficients of GDP per Capita (Models 4 and 5)

Model 4 is a random slope model that allows GDP per capita to vary across countries. Compared with model 1, only fixed effects coefficients of prospective

pocketbook evaluation and political sophistication change slightly. The intercept variance in model 4 is close to zero, and the random coefficient of GDP per capita is 0.313. That indicates that GDP per capita probably explains some of the variance across countries.

Model 5 is a random slope model with correlated variance. The fixed effects coefficients are the same as those in model 4. The intercept variance of model 5 (0.006) is greater than that in model 4, and the random coefficient of GDP per capita increases from 0.313 to 0.978. The between-country variance as a function of GDP per capita is as follows:

var(𝑢_0𝑗 + 𝑢_9𝑗𝐺𝐷𝑃_𝑖𝑗) = var(𝑢_0𝑗) + 2cov(𝑢_0𝑗𝑢_9𝑗)𝐺𝐷𝑃_𝑖𝑗 + var(𝑢_9𝑗)𝐺𝐷𝑃_𝑖𝑗2

= 0.006 − 0.154 𝐺𝐷𝑃𝑖𝑗 + 0.978 𝐺𝐷𝑃𝑖𝑗2

Figure 2.3 is the between-country variance as a function of GDP per capita. The between-country variance shows a linear increase as GDP per capita increases.

Nevertheless, the likelihood ratio test (assuming the uncorrelated equation model 4 is nested within the correlated equation model 5) is not significant (p = 1.000 > .05). It implies that the correlated variance model (model 5) is not necessarily more appropriate than the uncorrelated variance model (model 4). In addition, the likelihood ratio test (assuming the restricted equation model 1 is nested within the unrestricted equation model 5) is also not significant (p = 1.000 > .05). The two likelihood ratio tests demonstrate that the random effect of GDP per capita is not significant, and GDP per capita does not explain much between-country variance.

2.2.2.3 Random Coefficients of Polity Score and GDP Per Capita (Model 6)

Model 6 allows both polity score and GDP per capita to vary across nations. The fixed effects coefficients remain the same as those in model 1. Neither of those is

individually significant. The intercept variance is 0.053. The random coefficient of polity score is approximate to zero, and the random coefficient of GDP per capita is 0.004. Although the likelihood ratio tests of the previous models indicate that polity score and GDP per capita do not explain much between-country variance, the random coefficients of polity score and GDP per capita in model 6 indicate that GDP per capita probably explains more variance across countries than polity score.

2.3 RANDOM COEFFICIENTS ON A SUBSET OF POLITY SCORE DUMMIES