Factor Analysis homework help
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QUES 1:-
Each of 1524 patients of a medical center responded to 18 items of a 4-point questionnaire called the “Adult Behavior Checklist” (where each item response is scored: 1=Not at all true, 2 = Somewhat true, 3 = Rather true, 4 = Very True). The 18 items are listed below:
Item 1 - You fail to pay close attention to details or make careless mistakes in school, at work, etc.
Item 2 - You have difficulty sustaining your attention to tasks or in play activities.
Item 3 - You do not listen when directly spoken to.
Item 4 - You do not follow through on instructions and fail to finish schoolwork, chores, work duties, etc.
Item 5 - You have difficulty organizing tasks and activities.
Item 6 - You avoid, dislike, or are reluctant to engage in tasks that require sustained mental effort (e.g., homework
or schoolwork).
Item 7 - You lose things necessary for tasks or activities (e.g., books, school assignments, tools or keys).
Item 8 - You are easily distracted by extraneous stimuli (e.g., traffic noises, conversations, or looking out the
window).
Item 9 - You are forgetful in daily activities.
Item 10 - You fidget with your hands or feet and squirm in your seat.
Item 11 - You leave your seat in class or in other situations when remaining seated is expected.
Item 12 - You feel restless in situations where you are required to be still and quiet.
Item 13 - You have difficulty playing or engaging in leisure activities quietly.
Item 14 - You are “on the go” or act as if “driven by a motor”.
Item 15 - You talk excessively.
Item 16 - You blurt out answers before questions have been completed.
Item 17 - You have difficulty awaiting your turn.
Item 18 - You interrupt or intrude on others (e.g., butt into conversations or activities).
A researcher hypothesizes two models.
Model 1:
Items 1 through 9 form one factor (inattention), and items 13 through 18 measure a second factor (excitability). Also, these two factors are uncorrelated.
Model 2:
Items 1 through 9 form one factor (inattention), and items 13 through 18 measure a second factor (excitability). Also, these two factors are correlated.
Analyze both the models in detail.
ADHD Example
Model 1: 15 Items in either one of two uncorrelated factors; with uncorrelated errors.
Factor Equation:
Covariance Equation:
With Factor Covariance Matrix: and Error Covariance Matrix:
Model 2: 15 Items in either one of two correlated factors; with uncorrelated errors.
Model 2 uses the same exact set of equations as model 1,
except that the factor covariance matrix allows for correlation between the two factors,
by adding (not constraining) parameters in the following matrix:
Model Selection
Clearly, for a given set of test data, there are many such hypotheses, each hypothesis represented by a model composed of a set of linear structural equations. The idea is to test/compare these hypotheses (models) through fit statistics (e.g., chi-square, cross-validation) and model selection criteria (e.g., Akaike’s Information Criterion, AIC).
To test these hypotheses, the following presents the EQS command file and output for confirmatory factor analysis.
Model 1 output file
/TITLE
Model built by EQS 6 for Windows You need to first read in
ADHD.sav dataset into EQS.
/SPECIFICATIONS
DATA=’C:\EPSY COURSES\EPSY 583\adhd.ESS’;
VARIABLES=18; CASES=1524;
METHOD=ML; ANALYSIS=COVARIANCE; MATRIX=RAW; /LABELS
V1=ADHD1; V2=ADHD2; V3=ADHD3; V4=ADHD4; V5=ADHD5;
V6=ADHD6; V7=ADHD7; V8=ADHD8; V9=ADHD9; V10=ADHD10;
V11=ADHD11; V12=ADHD12; V13=ADHD13; V14=ADHD14; V15=ADHD15;
V16=ADHD16; V17=ADHD17; V18=ADHD18;
/EQUATIONS
V1 = 1F1 + E1;
V2 = *F1 + E2;
V3 = *F1 + E3;
V4 = *F1 + E4;
V5 = *F1 + E5;
V6 = *F1 + E6;
V7 = *F1 + E7;
V8 = *F1 + E8;
V9 = *F1 + E9;
V13 = 1F2 + E13;
V14 = *F2 + E14;
V15 = *F2 + E15;
V16 = *F2 + E16;
V17 = *F2 + E17;
V18 = *F2 + E18;
/VARIANCES
F1 = *;
F2 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E13 = *;
E14 = *;
E15 = *;
E16 = *;
E17 = *;
E18 = *;
/COVARIANCES
FIT=ALL;
TABLE=EQUATION;
/OUTPUT
Parameters;
Standard Errors;
RSquare;
Listing;
DATA=’EQSOUT.ETS’;/END
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE = 4541.528 ON 105 DEGREES OF FREEDOM
INDEPENDENCE AIC = 4331.52801 INDEPENDENCE CAIC = 3668.22071
MODEL AIC = 483.89013 MODEL CAIC = -84.65899 Significant model misfit
CHI-SQUARE = 663.890 BASED ON 90 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 663.084.
FIT INDICES
BENTLER-BONETT NORMED FIT INDEX = .854
BENTLER-BONETT NON-NORMED FIT INDEX= .849
COMPARATIVE FIT INDEX (CFI)= .871
BOLLEN (IFI) FIT INDEX= .871
MCDONALD (MFI) FIT INDEX= .827
LISREL GFI FIT INDEX= .945
LISREL AGFI FIT INDEX= .926
ROOT MEAN-SQUARE RESIDUAL (RMR)= .054
STANDARDIZED RMR= .102
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA)= .065
90% CONFIDENCE INTERVAL OF RMSEA (.060, .070)
MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY)
STANDARDIZED SOLUTION: R-SQUARED
ADHD1 =V1 = .537 F1 + .843 E1 .289
ADHD2 =V2 = .550*F1 + .835 E2 .303
ADHD3 =V3 = .479*F1 + .878 E3 .229
ADHD4 =V4 = .532*F1 + .847 E4 .283
ADHD5 =V5 = .521*F1 + .854 E5 .271
ADHD6 =V6 = .542*F1 + .841 E6 .293
ADHD7 =V7 = .497*F1 + .868 E7 .247
ADHD8 =V8 = .463*F1 + .887 E8 .214
ADHD9 =V9 = .616*F1 + .788 E9 .380
ADHD13 =V13 = .501 F2 + .866 E13 .251
ADHD14 =V14 = .410*F2 + .912 E14 .168
ADHD15 =V15 = .604*F2 + .797 E15 .364
ADHD16 =V16 = .647*F2 + .763 E16 .418
ADHD17 =V17 = .692*F2 + .722 E17 .479
ADHD18 =V18 = .619*F2 + .786 E18 .383
Model 2 output file
/TITLE
Model built by EQS 6 for Windows
/SPECIFICATIONS
DATA=’C:\EPSY COURSES\EPSY 583\adhd.ESS’;
VARIABLES=18; CASES=1524;
METHOD=ML; ANALYSIS=COVARIANCE; MATRIX=RAW;
/LABELS
V1=ADHD1; V2=ADHD2; V3=ADHD3; V4=ADHD4; V5=ADHD5;
V6=ADHD6; V7=ADHD7; V8=ADHD8; V9=ADHD9; V10=ADHD10;
V11=ADHD11; V12=ADHD12; V13=ADHD13; V14=ADHD14; V15=ADHD15;
V16=ADHD16; V17=ADHD17; V18=ADHD18;
/EQUATIONS
V1 = 1F1 + E1;
V2 = *F1 + E2;
V3 = *F1 + E3;
V4 = *F1 + E4;
V5 = *F1 + E5;
V6 = *F1 + E6;
V7 = *F1 + E7;
V8 = *F1 + E8;
V9 = *F1 + E9;
V13 = 1F2 + E13;
V14 = *F2 + E14;
V15 = *F2 + E15;
V16 = *F2 + E16;
V17 = *F2 + E17;
V18 = *F2 + E18;
/VARIANCES
F1 = *;
F2 = *;
E1 = *;
E2 = *;
E3 = *;
E4 = *;
E5 = *;
E6 = *;
E7 = *;
E8 = *;
E9 = *;
E13 = *;
E14 = *;
E15 = *;
E16 = *;
E17 = *;
E18 = *;
/COVARIANCES
F1,F2 = *;
FIT=ALL;
TABLE=EQUATION;
/OUTPUT
Parameters;
Standard Errors;
RSquare;
Listing;
DATA=’EQSOUT.ETS’;
/END
GOODNESS OF FIT SUMMARY FOR METHOD = ML
INDEPENDENCE MODEL CHI-SQUARE = 4541.528 ON 105 DEGREES OF FREEDOM
INDEPENDENCE AIC = 4331.52801 INDEPENDENCE CAIC = 3668.22071
MODEL AIC = 292.29048 MODEL CAIC = -269.94143
CHI-SQUARE = 470.290 BASED ON 89 DEGREES OF FREEDOM
PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS .00000
THE NORMAL THEORY RLS CHI-SQUARE FOR THIS ML SOLUTION IS 489.307.
FIT INDICES
BENTLER-BONETT NORMED FIT INDEX = .896
BENTLER-BONETT NON-NORMED FIT INDEX = .899
COMPARATIVE FIT INDEX (CFI) = .914
BOLLEN (IFI) FIT INDEX = .914
MCDONALD (MFI) FIT INDEX = .881
LISREL GFI FIT INDEX = .958
LISREL AGFI FIT INDEX = .944
ROOT MEAN-SQUARE RESIDUAL (RMR) = .026
STANDARDIZED RMR = .045
ROOT MEAN-SQUARE ERROR OF APPROXIMATION (RMSEA) = .053
90% CONFIDENCE INTERVAL OF RMSEA (.049, .058)
STANDARDIZED SOLUTION: R-SQUARED
ADHD1 =V1 = .533 F1 + .846 E1 .284
ADHD2 =V2 = .546*F1 + .838 E2 .298
ADHD3 =V3 = .484*F1 + .875 E3 .235
ADHD4 =V4 = .538*F1 + .843 E4 .289
ADHD5 =V5 = .512*F1 + .859 E5 .262
ADHD6 =V6 = .538*F1 + .843 E6 .290
ADHD7 =V7 = .504*F1 + .864 E7 .254
ADHD8 =V8 = .468*F1 + .884 E8 .219
ADHD9 =V9 = .615*F1 + .789 E9 .378
ADHD13 =V13 = .508 F2 + .862 E13 .258
ADHD14 =V14 = .386*F2 + .922 E14 .149
ADHD15 =V15 = .586*F2 + .810 E15 .343
ADHD16 =V16 = .640*F2 + .768 E16 .410
ADHD17 =V17 = .707*F2 + .707 E17 .500
ADHD18 =V18 = .631*F2 + .776 E18 .398
CORRELATIONS AMONG INDEPENDENT VARIABLES
V F
I F2 - F2 .451*I
I F1 - F1 I
I I