Statistics
Please write the Method which is in red. Please read the project description carefully in order to make a good description of the method. Alpha level used was .05 as confidence level. We alsolooked at the deviance and variance level, prority having the deviance.
We took consideration for group-mean centering, uncentered and grand-mean centering of variables. (For this please do some reaserch tofind what they each mean in HLM modeling).The dumy variables make sense to be uncentered. The dumy variables wore Gender and Private,they are categoricals variables. Col_n was switch with logn.
Attached is also a copy of one of the models and the results, but this is just a reference for you, and not to include numbers from that in this section.
Your Method section (1-2 pages) should be very brief on participants and variables. Devote most of your section to describing the models that will be employed to test your specific research question(s). Include information as appropriate for alpha levels to be used, etc. Do not include actual output or results.
Project (HLM)
Specify and run the following HLM model and interpret your results. Refine the model as appropriate. Use st_data_project.sav for Level 1 data and col_data_project.sav for Level 2 data.
Outcome = st_gpa1
Level-1 Model
Y = B0 + B1*(GENDER) + B2*(HSCGPA) + B3*(BESTTEST) + R
Level-2 Model
B0 = G00 + G01*(COL_N) + G02*(SELRATIO) + G03*(PRIV) + U0
B1 = G10 + U1
B2 = G20 + G21*(COL_N) + G22*(SELRATIO) + G23*(STFACRAT) + U2
B3 = G30 + U3
The project data consist of individual-level and school-level variables for 5,762 students at 130 colleges.
Individual-level data (SPSS data file = st_data_project.sav):
col_id College 8-digit ID
st_gpa1 Student GPA during first year in college. Should range from 0 to 4. Could be used as an outcome variable.
gender Student gender (1=male, 0=female)
st_cred1 Credit hours earned by student during first year in college. Could be used as an outcome variable. Another possible outcome variable would be first-year quality points (st_gpa1*st_cred1 for each student).
hscgpa High-school GPA in core academic classes. Can range from 0 to 5 (values of >4 due to advanced placement coursework).
hsunits Number of core academic classes taken in high school.
besttest Best score on ACT or SAT during high school (converted to SAT-units).
graduate Did student graduate from college within 6 years? Graduates=1, non-graduates=0. Could be used as an outcome variable for a generalized linear model.
testz besttest converted to a z-score metric based on mean=1017 and sd=207. Could be used in place of besttest if model has estimation problems due to large variance of besttest in comparison to other level-1 variables.
test10 Besttest divided by 10 (trailing zero removed from besttest). Could be used in place of besttest as described for testz, but may be more understandable than testz.
College-level data (SPSS data file = col_data_project.sav):
col_id College 8-digit ID
col_n Undergraduate enrollment at college (full-time and part-time). Due to the magnitude of the variance of this variable in comparison to other level-2 variables, the logn variable should probably be used in place of col_n.
selratio Admissions selectivity of the college (100 times the ratio of the number of acceptances divided by the number of applications received). Numbers closer to 100 indicate less selectivity; numbers closer to 0 indicate more selectivity.
stfacrat Student-faculty ratio (number of undergraduate students divided by number of faculty at the college). Higher numbers indicate greater numbers of students present for each existing faculty member.
cost Cost of attendance for an out-of-state student (dollars). Due to the magnitude of the variance of this variable in comparison to other level-2 variables, the logcost variable should probably be used in place of cost.
col_grad Student body 6-year graduation rate (0 to 100).
priv Institution public/private status. 0=public, 1=private.
col_test Average student HS test score (SAT-unit scaling) at that college. Due to the magnitude of the variance of this variable in comparison to other level-2 variables, the coltst10 or col_ztst variable should probably be used in place of col_test.
coltst10 col_test divided by 10. Could be used in place of col_test to remedy estimation problems that may arise due to large variance of col_test variable.
col_ztst col_test converted to a z-score based on mean=1017 and sd=207. Could be used in place of col_test to remedy estimation problems that may arise due to large variance of col_test variable.
logcost Base 10 logarithm of cost. Could be used in place of cost to remedy estimation problems that may arise due to large variance of cost variable.
logn Base 10 logarithm of col_n. Could be used in place of col_n to remedy estimation problems that may arise due to large variance of col_n variable.
Note that several mentions have been made of estimation problems that could arise due to variable scaling. This is most likely to arise in the level-2 model due to inclusion of col_test, col_n or cost and appears to be a result of the very large variances of these variables as compared to the other level-2 variables. Re-scaled versions of col_test, col_n and cost have been provided and their inclusion in place of the originals seems to remedy any problems. A similar estimation problem often arises in SEM programs when the ratio of variances for variables within a factor differ by a ratio of more than 10 to 1 or 100 to 1. If there is a HLM estimation problem, you will notice in the output that the program never makes it to the iterations and displays a message like “Matrix Vtheta1 is not invertible. Unable to continue.”
Specifications for HLM Mini-Project
• Papers should be no longer than 5-10 pages (excluding references and appendices).
• All papers should be formatted as follows:
? Reporting of test statistics in the paper text
? General formatting and numbering of tables and figures
? Section headings (Introduction, Results, etc.)
? Form of references and proper use of references
? Economy and logical flow of expression in the text including appropriate verb tenses within each section
? Times New Roman font 11-12 pt
? Double spaced
• Tables/figures of import (i.e., those referenced in your results) should probably be included within the text. If necessary, include longer sets of tables as appendices. Note, however, that I do not want large amounts of program output attached as an appendix.
• Your Introduction section (1 or 2 paragraphs) should clearly delineate the topic of your study and your specific research questions.
• Your Method section (1-2 pages) should be very brief on participants and variables. Devote most of your section to describing the models that will be employed to test your specific research question(s). Include information as appropriate for alpha levels to be used, etc. Do not include actual output or results.
• Your Results section (2-5 pages) should provide answers to your research question(s). Include appropriate output/tables/graphs as necessary.
• Your Discussion section (2-5 paragraphs) should present a thoughtful critique (but not a simple restatement) of your results, including any deficiencies in the study/questions/analyses, etc.
• Papers will be evaluated primarily on correctness, completeness, and conciseness.
Grades will be determined using the following equally-weighted criteria:
• Accuracy: Data are analyzed using the correct tests and the procedure yields the correct results.
• Interpretation: All results are correctly interpreted.
• Presentation: Results are presented clearly and concisely. All of the appropriate and relevant information is included, but the narrative is free of jargon and extraneous information.
• Professional format: Format of the paper is professional and tables are clear and concise. (PLEASE DO NOT ENCLOSE YOUR PAPER IN A BINDER OR PLASTIC COVER).
• Professional writing: Title page is included and professionally formatted. Writing is free of grammar, spelling, and mechanical errors. Entire paper is professionally prepared.
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