/* ---------------------------------------------------------
	FILE: cfa.nfactors.nmtwins.sas

	DATA: National Merit Twin data

	Purpose: Using CFA and maximum likelihood to estimate
		the number of factors. NOTE VERY WELL: This code
		is useful only for checking the number of factors.
		It is NOT useful for interpreting the loadings.
  ---------------------------------------------------------- */

* - NOTE: Assign LIBNAME p7291 to the directory/folder
	containing the Natinoal Merit Twin data;
*LIBNAME p7291 '';

OPTIONS NOCENTER NODATE PAGENO=1;

/* --- Two very important issue about uncovering the number of factors:
  		(1) No correlations among the factors
  		(2) Set loadings to 0 as shown below:
  			(2a) first factor = all free loadings
  			(2b) second factor = 0 loading on first variable
  			(2c) third factor  = 0 loadings on first and second variable
  			(2d) fourth factor = 0 loadings on first, second & third vars
  			(2e) etc.
    --- */
		
TITLE  National Merit Twins: Confirmatory Factor Analysis;
TITLE2 Two Factor Solution;
PROC CALIS DATA=nmtdir.nmttest CORR PRINT;
	VAR English -- Vocab;
	LINEQS
		English = lam11 F1 +     0 F2 + e_Eng,
		Math    = lam21 F1 + lam22 F2 + e_Math,
		SocSci  = lam31 F1 + lam32 F2 + e_SS,
		NatSci  = lam41 F1 + lam42 F2 + e_NS,
		Vocab   = lam51 F1 + lam52 F2 + e_Voc;
	STD
		F1 = V_F1,
		F2  = V_F2,
		e_Eng   = V_eEng,
		e_Math  = V_eMath,
		e_SS    = V_eSS,
		e_NS    = V_eNS,
		e_Voc   = V_eVoc;
	* - constraints: set 1: constraints needed to identify the model;
		V_F1 = 1;
		V_F2  = 1;
RUN;


TITLE2 One Factor Solution;
PROC CALIS DATA=nmtdir.nmttest CORR PRINT;
	VAR English -- Vocab;
	LINEQS
		English = lam11 F1 + e_Eng,
		Math    = lam21 F1 + e_Math,
		SocSci  = lam31 F1 + e_SS,
		NatSci  = lam41 F1 + e_NS,
		Vocab   = lam51 F1 + e_Voc;
	STD
		F1 = V_F1,
		e_Eng   = V_eEng,
		e_Math  = V_eMath,
		e_SS    = V_eSS,
		e_NS    = V_eNS,
		e_Voc   = V_eVoc;
	* - constraints: set 1: constraints needed to identify the model;
		V_F1 = 1;
RUN;