#### I checked through every 3 factor * 3 loading case.
#### While, 4 factor * 3 loading failed.
#### the data is 6 factor * 3 loading

require(sem);

cor18<-read.moments();
1
.68 1
.60 .58 1
.01 .10 .07 1
.12 .04 .06 .29 1
.06 .06 .01 .35 .24 1
.09 .13 .10 .05 .03 .07 1
.04 .08 .16 .10 .12 .06 .25 1
.06 .09 .02 .02 .09 .16 .29 .36 1
.23 .26 .19 .05 .04 .04 .08 .09 .09 1
.11 .13 .12 .03 .05 .03 .02 .06 .06 .40 1
.16 .09 .09 .10 .10 .02 .04 .12 .15 .29 .20 1
.24 .26 .22 .14 .06 .10 .06 .07 .08 .03 .04 .02 1
.21 .22 .29 .07 .05 .17 .12 .06 .06 .03 .12 .04 .55 1
.29 .28 .26 .06 .07 .05 .06 .15 .20 .10 .03 .12 .64 .61 1
.15 .16 .19 .18 .08 .07 .08 .10 .06 .15 .16 .07 .25 .25 .16 1
.24 .20 .16 .13 .15 .18 .19 .18 .14 .11 .07 .16 .19 .21 .22 .35 1
.14 .25 .12 .09 .11 .09 .09 .11 .21 .17 .09 .05 .21 .23 .18 .39 .48 1

mod3.1_9<-specify.model();
X1  <-> X1,TD11,NA
X2  <-> X2,TD22,NA
X3  <-> X3,TD33,NA
X4  <-> X4,TD44,NA
X5  <-> X5,TD55,NA
X6  <-> X6,TD66,NA
X7  <-> X7,TD77,NA
X8  <-> X8,TD88,NA
X9  <-> X9,TD99,NA
X1  <- xi1,LY11, NA
X2  <- xi1,LY21, NA
X3  <- xi1,LY31, NA
X4  <- xi2,LY42, NA
X5  <- xi2,LY52, NA
X6  <- xi2,LY62, NA
X7  <- xi3,LY73, NA
X8  <- xi3,LY83, NA
X9  <- xi3,LY93, NA
xi1  <-> xi1,NA,1
xi2  <-> xi2,NA,1
xi3  <-> xi3,NA,1
xi1  <-> xi2 ,PH12,NA
xi1  <-> xi3 ,PH13,NA
xi2  <-> xi3 ,PH23,NA

mod3.1_6AND10_12<-specify.model();
X1  <-> X1,TD11,NA
X2  <-> X2,TD22,NA
X3  <-> X3,TD33,NA
X4  <-> X4,TD44,NA
X5  <-> X5,TD55,NA
X6  <-> X6,TD66,NA
X10  <-> X10,TD77,NA
X11  <-> X11,TD88,NA
X12  <-> X12,TD99,NA
X1  <- xi1,LY11, NA
X2  <- xi1,LY21, NA
X3  <- xi1,LY31, NA
X4  <- xi2,LY42, NA
X5  <- xi2,LY52, NA
X6  <- xi2,LY62, NA
X10  <- xi3,LY73, NA
X11  <- xi3,LY83, NA
X12  <- xi3,LY93, NA
xi1  <-> xi1,NA,1
xi2  <-> xi2,NA,1
xi3  <-> xi3,NA,1
xi1  <-> xi2 ,PH12,NA
xi1  <-> xi3 ,PH13,NA
xi2  <-> xi3 ,PH23,NA

mod3.1_3AND7_9AND10_12<-specify.model();
X1  <-> X1,TD11,NA
X2  <-> X2,TD22,NA
X3  <-> X3,TD33,NA
X10  <-> X10,TD44,NA
X11  <-> X11,TD55,NA
X12  <-> X12,TD66,NA
X7  <-> X7,TD77,NA
X8  <-> X8,TD88,NA
X9  <-> X9,TD99,NA
X1  <- xi1,LY11, NA
X2  <- xi1,LY21, NA
X3  <- xi1,LY31, NA
X10  <- xi2,LY42, NA
X11  <- xi2,LY52, NA
X12  <- xi2,LY62, NA
X7  <- xi3,LY73, NA
X8  <- xi3,LY83, NA
X9  <- xi3,LY93, NA
xi1  <-> xi1,NA,1
xi2  <-> xi2,NA,1
xi3  <-> xi3,NA,1
xi1  <-> xi2 ,PH12,NA
xi1  <-> xi3 ,PH13,NA
xi2  <-> xi3 ,PH23,NA

mod3.4_6AND7_9AND10_12<-specify.model();
X10  <-> X10,TD11,NA
X11  <-> X11,TD22,NA
X12  <-> X12,TD33,NA
X4  <-> X4,TD44,NA
X5  <-> X5,TD55,NA
X6  <-> X6,TD66,NA
X7  <-> X7,TD77,NA
X8  <-> X8,TD88,NA
X9  <-> X9,TD99,NA
X10  <- xi1,LY11, NA
X11  <- xi1,LY21, NA
X12  <- xi1,LY31, NA
X4  <- xi2,LY42, NA
X5  <- xi2,LY52, NA
X6  <- xi2,LY62, NA
X7  <- xi3,LY73, NA
X8  <- xi3,LY83, NA
X9  <- xi3,LY93, NA
xi1  <-> xi1,NA,1
xi2  <-> xi2,NA,1
xi3  <-> xi3,NA,1
xi1  <-> xi2 ,PH12,NA
xi1  <-> xi3 ,PH13,NA
xi2  <-> xi3 ,PH23,NA

mod4<-specify.model();
X1  <-> X1,TD11,NA
X2  <-> X2,TD22,NA
X3  <-> X3,TD33,NA
X4  <-> X4,TD44,NA
X5  <-> X5,TD55,NA
X6  <-> X6,TD66,NA
X7  <-> X7,TD77,NA
X8  <-> X8,TD88,NA
X9  <-> X9,TD99,NA
X10 <-> X10,TDaa,NA
X11 <-> X11,TDbb,NA
X12 <-> X12,TDcc,NA
X1  <- xi1,LY11, NA
X2  <- xi1,LY21, NA
X3  <- xi1,LY31, NA
X4  <- xi2,LY42, NA
X5  <- xi2,LY52, NA
X6  <- xi2,LY62, NA
X7  <- xi3,LY73, NA
X8  <- xi3,LY83, NA
X9  <- xi3,LY93, NA
X10 <- xi4,LXa4,NA
X11 <- xi4,LXb4,NA
X12 <- xi4,LXc4,NA
xi1  <-> xi1,NA,1
xi2  <-> xi2,NA,1
xi3  <-> xi3,NA,1
xi4  <-> xi4,NA,1
xi1  <-> xi2 ,PH12,NA
xi1  <-> xi3 ,PH13,NA
xi2  <-> xi3 ,PH23,NA
xi4  <-> xi1,PH41,NA
xi4  <-> xi2,PH42,NA
xi4  <-> xi3,PH43,NA

summary(sem(mod3.1_9,cor18,500))$RMSEA;
summary(sem(mod3.1_6AND10_12,cor18,500))$RMSEA;
summary(sem(mod3.1_3AND7_9AND10_12,cor18,500))$RMSEA;
summary(sem(mod3.4_6AND7_9AND10_12,cor18,500))$RMSEA;
summary(sem(mod4,cor18,500))$RMSEA;##fail

	[[alternative HTML version deleted]]

