Reference no: EM132722808
Section 1: Factors associated with students' performance
Use the "Academic awards.sav" file.
A research conducted a research to determine whether the number of awards a student received is explained by (1) the student's math score and (2) the type of program taught at school (coded as prog 1: general, prog 2: academic prog 3: vocational program).
QUESTION 1
Test whether the dependent variable "number of awards" follows a Poisson distribution
Fit a Poisson model Generalized Linear Model. Answer questions 2-6 (Section 1) from the SPSS output you obtained.
QUESTION 2
Are the mean and variance values for the dependent variable similar?
QUESTION 3
Is the deviance/df value of this model acceptable? Justify your answer.
QUESTION 4
What does the Likelihood Ratio Chi-Square statistics actually tests? What do you conclude from this test?
QUESTION 5
Is the variable "math" significantly associated with the dependent variable? Interpret the Exp(B) value.
QUESTION 6
Compare the performance of students in "Program 1" with those in "Program 3". Is the sign of the "B" estimate of the "prog=1" group positive or negative? What does this sign mean? Interpret the Exp(B) estimate for this group.
Now, fit two negative binomial regression models: in the first model set the "ancillary parameter" equal to 1 (default model), and in the second fit the model based on the estimated "ancillary parameter". Answer question 7 below.
QUESTION 7
Construct a table that summarizes all the fitted 3 models as shown below. From this table determine what is the best model to choose. Justify your answer.
Model comparison table
Model
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Deviance
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Pearson chi-square
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LL
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AIC
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BIC
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Deviance/df
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Pearson chisq/df
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1
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Poisson
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2
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NB(default)
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3
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NB (estimated
ancillary parameter)
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Section 2: Differences between Study program
Use the "Academic awards.sav" file.
A researcher wanted to determine whether there were differences in Mathematics and English score between the students from three different school programs (coded as prog 1: general, prog 2: academic prog 3: vocational program).
QUESTION 1
Test whether the dependent variables "English" and "Maths" follow normal distribution. Based on the information provided what is your assessment regarding this assumption for: English and maths score?
Fit a MANOVA Model. Answer questions 2-6 (Section 2) from the SPSS output you obtained.
QUESTION 2
What is the mean value for the Maths and English score for each program?
QUESTION 3
Test the assumption that covariance matrices are statistically similar? What do you conclude from this test?
QUESTION 4
From the "multivariate test" table, determine whether programs have different effects on Math and English score. State your reason clearly?
QUESTION 5
From the univariate analysis Table, determine whether Maths and English score differ between the programs. What do you conclude from this test?
a. Is there a difference in maths score?
b. Is there a difference in English score?