Engagement Views Secondary Analysis
Joshua Rosenberg
7/16/2017
Final model
Processing other data
Overall model
For some reason, we get a different overall model when we use the population-level (not ID, i.e. not student but overall) predictions. There’s also some code for using the equation.
Some other representations of models
Here’s one using the student-level predictions.
In these models, the intercepts and slopes are adjusted based on the random effects for those terms.
Look out, lots going on.
We can color these by something like final grade.
We can also do this by something like cost value, which was recoded from the data I had (a file with all three semesters), so higher levels represent not higher cost but lower cost. But, that’s a bit confusing, because the top lines seem to be associated with lower levels of cost-value, i.e., they had to give up a lot for the course. I guess that could be because they’re putting in time.
Or by grade quartiles. It looks like those in quartile 3 (not 4, which is the highest) may have a higher intercept.
Models
E-V predicting curves
Here are some models, first for antecedents of different intercepts and slopes.
##
## Call:
## lm(formula = intercept ~ task_value * perceived_competence, data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -11.783 -6.266 -2.551 4.763 42.061
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.5473 25.0690 0.062 0.951
## task_value 2.9146 6.2361 0.467 0.641
## perceived_competence 1.4122 6.2882 0.225 0.822
## task_value:perceived_competence -0.4395 1.5087 -0.291 0.771
##
## Residual standard error: 8.844 on 248 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.004028, Adjusted R-squared: -0.00802
## F-statistic: 0.3343 on 3 and 248 DF, p-value: 0.8005##
## Call:
## lm(formula = linear_slope ~ task_value * perceived_competence,
## data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -10.383 -1.171 0.717 1.650 3.123
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.27791 6.47899 0.043 0.966
## task_value -0.61472 1.61170 -0.381 0.703
## perceived_competence -0.28079 1.62517 -0.173 0.863
## task_value:perceived_competence 0.08605 0.38991 0.221 0.826
##
## Residual standard error: 2.286 on 248 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.003428, Adjusted R-squared: -0.008627
## F-statistic: 0.2844 on 3 and 248 DF, p-value: 0.8367##
## Call:
## lm(formula = quadratic_slope ~ task_value * perceived_competence,
## data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.19012 -0.10156 -0.04411 0.07029 0.61819
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.020291 0.392970 -0.052 0.959
## task_value 0.034424 0.097754 0.352 0.725
## perceived_competence 0.015377 0.098571 0.156 0.876
## task_value:perceived_competence -0.004658 0.023649 -0.197 0.844
##
## Residual standard error: 0.1386 on 248 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.003247, Adjusted R-squared: -0.008811
## F-statistic: 0.2693 on 3 and 248 DF, p-value: 0.8475Just tried a different type of value - utility value in this case.
E-V predicting final grades
Here are models with the antecedents predicting final grade
m3 <- lm(final_grade ~ task_value * perceived_competence, data = dfm_b)
summary(m3)##
## Call:
## lm(formula = final_grade ~ task_value * perceived_competence,
## data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.019 -7.050 1.993 7.841 20.421
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.364 29.427 0.386 0.6997
## task_value 14.918 7.320 2.038 0.0426 *
## perceived_competence 14.440 7.381 1.956 0.0515 .
## task_value:perceived_competence -2.836 1.771 -1.601 0.1106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.38 on 248 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.09329, Adjusted R-squared: 0.08232
## F-statistic: 8.506 on 3 and 248 DF, p-value: 2.125e-05m4 <- lm(final_grade ~ task_value * perceived_competence, data = dfm_b)
summary(m4)##
## Call:
## lm(formula = final_grade ~ task_value * perceived_competence,
## data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.019 -7.050 1.993 7.841 20.421
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 11.364 29.427 0.386 0.6997
## task_value 14.918 7.320 2.038 0.0426 *
## perceived_competence 14.440 7.381 1.956 0.0515 .
## task_value:perceived_competence -2.836 1.771 -1.601 0.1106
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.38 on 248 degrees of freedom
## (20 observations deleted due to missingness)
## Multiple R-squared: 0.09329, Adjusted R-squared: 0.08232
## F-statistic: 8.506 on 3 and 248 DF, p-value: 2.125e-05Also looked at outcomes. Adjusted the linear term to be associated with changes per day, though I’m still having a hard time interpreting these coefficients. That said, it doesn’t look like the intercept is (linearly) associated with lower final grades, which is somewhat surprising, but maybe not entirely because quartile 3 demonstrated higher final grades.
##
## Call:
## lm(formula = final_grade ~ intercept + linear_slope + quadratic_slope,
## data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -33.468 -5.976 0.676 7.074 20.948
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 42.837 11.305 3.789 0.000189 ***
## intercept 15.022 5.738 2.618 0.009375 **
## linear_slope 182.163 91.424 1.993 0.047395 *
## quadratic_slope 2057.691 1146.074 1.795 0.073784 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.542 on 252 degrees of freedom
## (16 observations deleted due to missingness)
## Multiple R-squared: 0.2278, Adjusted R-squared: 0.2186
## F-statistic: 24.78 on 3 and 252 DF, p-value: 4.38e-14##
## Call:
## lm(formula = final_grade ~ intercept, data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -39.661 -6.764 1.392 7.962 20.833
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 82.37970 1.11860 73.645 <2e-16 ***
## intercept 0.13692 0.07643 1.791 0.0744 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.75 on 254 degrees of freedom
## (16 observations deleted due to missingness)
## Multiple R-squared: 0.01248, Adjusted R-squared: 0.008589
## F-statistic: 3.209 on 1 and 254 DF, p-value: 0.07442##
## Call:
## lm(formula = final_grade ~ linear_slope, data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.391 -6.922 1.715 8.025 20.552
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 83.4669 0.8812 94.720 <2e-16 ***
## linear_slope -0.2702 0.2972 -0.909 0.364
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.8 on 254 degrees of freedom
## (16 observations deleted due to missingness)
## Multiple R-squared: 0.003244, Adjusted R-squared: -0.0006807
## F-statistic: 0.8266 on 1 and 254 DF, p-value: 0.3641##
## Call:
## lm(formula = final_grade ~ quadratic_slope, data = dfm_b)
##
## Residuals:
## Min 1Q Median 3Q Max
## -40.584 -6.974 1.888 8.013 20.430
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 83.6606 0.8445 99.071 <2e-16 ***
## quadratic_slope 3.1096 4.9038 0.634 0.527
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.81 on 254 degrees of freedom
## (16 observations deleted due to missingness)
## Multiple R-squared: 0.001581, Adjusted R-squared: -0.00235
## F-statistic: 0.4021 on 1 and 254 DF, p-value: 0.5266