## 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