Question: 102

a. FILL IN THE BLANK: In Y^ = b₁X₁ + b₂X₂ where X₁ and X₂ are not correlated, VIF for X₁ is ___0______ and

VIF for X₂ is ____0____________.

b. In Y^ = b₁X₁ + b₂X₂, VIF for X₁ is always the same as VIF for X₂. Very briefly explain why.

Solution: This is because

\[VI{{F}_{1}}=\frac{1}{1-R_{1,2}^{2}},\,\,\,\,VI{{F}_{2}}=\frac{1}{1-R_{2,1}^{2}}\]

where \(R_{1,2}^{2}=R_{2,1}^{2}=r\), the correlation between X₁ and X₂, so \(VI{{F}_{1}}=VI{{F}_{2}}\).

Factor Analysis:

101.1

In 2006 GSS, they asked some questions on attitudes toward gun control. They asked the following

seven questions.

1. GUNSALES should background check be required for private gun sale

2. GUNSDRUG should penalty for illegal gun sale be tougher than drug

3. SEMIGUNS should semi-auto gun sale be limited to military

4. GUNS911 should gun control law be stricter after 911

5. RIFLES50 should high power rifle sale be limited to military

6. OTHGUNS number of adult owing a gun in household

7. GUNSDRNK should carrying a firearm drinking alcohol be illegal

You are trying to come up with a scale called “attitude toward gun control.”

a. GUNSDRUG is coded in a wrong order. Verify it, and recode by: recode gunsdrug (2=3)(3=2).

Hint: If you find “preferences” or “options,” “pivot table labeling,” and change it to “values and labels,”

you see 1, 2, and 3 (values) in addition to “tougher,” “less tough,” and “about as tough.”

b. Run a frequency of all seven variables to make sure that all variables are coded correctly.

c. Make a guess on which of the following items would qualify for this single scale. Simply pick #’s out of seven (something like 1, 2, 3, 5, 7). There is no single correct answer. Explain your choice in a single sentence.

d. Run a factor analysis for 2006 respondents (select if year=2006), using ML estimation and OBLIMIN rotation. Which questions are retained for “attitude toward gun ownership?”

e. Does the empirical factor structure match your guess? Briefly explain.

f. You should have three questions to make up the scale. Check the mean and standard deviation of these three.

g. Do you need to “reverse code?” Check the direct of the three scale items and discuss if you need to reverse-code any. If you need to, do so.

h. Now create a scale which ranges from 1-5. Remember that these three questions are on different scales (1-5, 1-2, etc.). Change “123” to “135” and “12” to “15” (or “24”) to make three standard deviations approximately equal before making the scale. Show the process and SPSS commands.

Program so that you retain cases when they answered at least two questions.

i. Name the scale (implying a direction), and obtain the mean and standard deviation.