1st task: no software needed. Should be able to answer without anything if well versed in SEM (estimated time: 20 minutes). 2nd task: In this task, you will modify the SAS/IML program to compute the determinant of the model implied covariance matrix and the loglikelihood function value of Example 1 at each of the three sets of starting values (estimated time: 1.5-2 hours) If you do not have the IML program, you are welcome to use whatever software needed to ensure completion. Please see attached documents. Must have SAS in order to open dataset. Please review sheets before committing, as I will assume you know what you are doing. Please feel free to ask any questions.
Psyc 650/790 Homework 1 I need to determine the orders of 1) the vectors y and x for the observed variables, 2) the vectors η and ξ for the latent variables, and 3) the parameter matrices Λy, Θε, Λx, Θδ, B, Γ, Φ, and Ψ for the Y-side measurement model the X-side measurement model and the latent variable model Step 1 : Count the number of the Y-side observed variables so that you can determine the orders of ______ and ______. Step 2 : Count the number of the X-side observed variables so that you can determine the orders of ______ and ______. Step 3: Given the number of the Y-side observed variables and the number of the Y-side latent variables, you can determine the orders of ______, ______, ______, and ______. Step 4 : Finally, given the number of the X-side observed variables and the number of both the Y-side and the X-side latent variables, you can determine the orders of ______, ______, ______, and ______. 2 ( ) ( ) with Var and Var. =++== ηΒηΓξζξΦζΨ ( ) with Var, y e =+= y ΛηεεΘ ( ) with Var, x d =+= x ΛξδδΘ Psyc 650/790 Homework 1 you will modify the SAS/IML program to compute the determinant of the model implied covariance matrix and the loglikelihood function value of Example 1 at each of the three sets of starting values. Please write 5 digits after the decimal point. 2 Set 1 gamma11 = 0.3; gamma22 = 0.3; beta12 = 0.3; beta21 = 0.3; beta31 = 0.3; beta32 = 0.3; psi11 = 0.5; psi21 = 0.3; psi22 = 0.5; psi31 = 0.3; psi32 = 0.3; psi33 = 0.5; phi11 = 5; phi21 = 15; phi22 = 500; Set 2 gamma11 = 0; gamma22 = 0; beta12 = 0; beta21 = 0; beta31 = 0; beta32 = 0; psi11 = 0.5; psi21 = 0.3; psi22 = 0.5; psi31 = 0.3; psi32 = 0.3; psi33 = 0.5; phi11 = 5; phi21 = 15; phi22 = 500; Set 3 gamma11 = 0; gamma22 = 0; beta12 = 0; beta21 = 0; beta31 = 0; beta32 = 0; psi11 = 0.3; psi21 = 0.3; psi22 = 0.3; psi31 = 0.3; psi32 = 0.3; psi33 = 0.3; phi11 = 5; phi21 = 15; phi22 = 500; Let θi collect all the starting values and use det[Σ(θi)] to denote the determinant of the model implied covariance matrix for Set i (i = 1, 2, 3). For Set 1, det[Σ(θ1)] = _______________ FML = _______________ (2 points) For Set 2, det[Σ(θ2)] = _______________ FML = _______________ (2 points) For Set 3, det[Σ(θ2)] = _______________ (1 point) For Set 3, you may observe an error message when calculating FML, can you explain why FML for Set 3 is not computable? (1 point)