Set of Histograms - Equal Weight Index - Pairwise Correlations - Coefficients - Ordinal IRT Model - Statistics Assignment Help

Assignment Task:

Set of Histograms Statistics Assignment Help

10.2.1 Question 1 

10.2.1.1 A 

Construct a set of histograms for the trust_ variables and calculate the means of all the variables as well. Use these to describe the general features of the distributions of these indicator variables. 

10.2.1.2 B 

What are the arguments for treating the trust_ variables as interval level indicators? What are the arguments for treating them as ordinal-level indicators? 

10.2.1.3 C 

For the purposes of this analysis, the target concept that we would like to measure is “trust in institutions”, at the level of individuals. We will then make comparisons across individuals in the data with different values of the country, gender, age and degree. Briefly describe one potential limitation of any measure based on these indicators for making such comparisons. 

10.2.1.4 D 

Identify an alternative concept that you might have measured with a subset of these indicators. What is the concept, and which indicators would you use to measure that concept? 

10.2.2 Question 2 

10.2.2.1 A 

Construct an equal weight index using all seven trust_ variables. Fit a linear regression (lm()) with dummy variables for countries and include a weight=ess2018$weight argument so that you are using the survey weights. Describe general patterns in which countries’ citizens have higher and lower trust in institutions. 

10.2.2.2 B 

Do an analysis to assess whether the trust index varies as a function of age, gender and whether someone has a university degree. There are many ways you could do this, but whichever analysis you do, state clearly what you have done and what we can conclude about the relationship between trust and these other variables. 

10.2.3 Question 3

10.2.3.1 A 

Use cor() to examine the pairwise correlations between the trust_ variables. Describe any major patterns that you see. 

10.2.3.2 B 

Use promo() to do principal components analysis on the trust_ variables. Examine the coefficients and give an interpretation for the first principle component 

10.2.3.3 C 

Examine the coefficients and give an interpretation for the second and third principal components, if you are able to. 

10.2.3.4 D 

Create the scree plot for this principal components analysis. What do we learn from this? 

10.2.3.5 E 

Repeat the analysis from B, C, & D using only responses where ess2018$country == "United Kingdom". Does the within UK variation across individuals look similar to the across Europe variation in individuals? What is the same/different? 

10.2.4 Question 4

10.2.4.1 A 

If we used an ordinal IRT model to analyse these data, how would that change the assumptions that we are making from those made in the Principle Components Analysis above? How many difficulty and discrimination parameters would there be? 

10.2.4.2 B 

If we applied the ordinal IRT model, we would then have three different scores of individual-level trust: one based on equal weighting, one based on the first principle component, and one based on the ordinal IRT model. Without actually doing the comparison, would you expect the correlation between the three measures of individual measures to be high or low, given what we have seen across these analyses? Explain why. If you have been unable to do some/all of the above analyses, you still may be able to answer this question. 

10.2.5 Question 5

10.2.5.1 A 

Load the country-level averages from final-assessment-ess2018country.csv. Use kmeans clustering to identify two clusters of countries. What are the clusters that emerge? How would you label them? Repeat with three clusters, and describe how the countries are divided up differently into three groups versus two. 

10.2.5.2 B 

Given what you observed in A, do you think clustering countries into classes makes sense for these data? Why or why not? 

10.2.5.3 C 

What do we learn from the fact that these clusters emerge in a country-level analysis? How does this relate to what we learned from the individual-level analysis? Explain. 

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