Appendix A: Mplus syntax for the non-stationary manifest Markov model
TITLE: Manifest Markov model Ending letter Sounds
Heterogeneous transition probabilities with poverty added
Input for results in Table 1
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEVARIABLES ARE pov ending1 ending2 ending3 ending4 ;
CATEGORICAL ARE ending1 ending2 ending3 ending4;
classes c1(2) c2(2) c3(2) c4(2)
missing are .;
ANALYSIS:
TYPE = mixture missing;
MODEL:
%OVERALL%
[c2#1-c4#1] ;
c4#1 ON c3#1 ;
c3#1 ON c2#1 ;
c2#1 ON c1#1 ;
c4#1 ON POV;
c3#1 ON POV;
c2#1 ON POV;
c1#1 ON POV;
MODEL c1:
%c1#1%
[ending1$1@15] ;
%c1#2%
[ending1$1@-15] ;
MODEL c2:
%c2#1%
[ending2$1@15] ;
%c2#2%
[ending2$1@-15] ;
MODEL c3:
%c3#1%
[ending3$1@15] ;
%c3#2%
[ending3$1@-15] ;
MODEL c4:
%c4#1%
[ending4$1@15] ;
%c4#2%
[ending4$1@-15];
OUTPUT:
Appendix B: Mplus syntax for the stationary manifest Markov model with invariant response probabilities; Total sample
TITLE: Manifest Markov Model for Ending letter Sounds.
Homogeneous transition probabilities with poverty added
Input for upper panel of Table 2
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEVARIABLES ARE ending1 ending2 ending3 ending4;
CATEGORICAL ARE ending1 ending2 ending3 ending4;
classes c1(2) c2(2) c3(2) c4(2)
missing are .;
ANALYSIS:
TYPE = mixture missing;
MODEL:
%OVERALL%
[c1#1-c4#1] (1) ;
c4#1 ON c3#1 (2) ;
c3#1 ON c2#1 (2);
c2#1 ON c1#1 (2);
MODEL c1:
%c1#1%
[ending1$1@15] (3);
%c1#2%
[ending1$1@-15] (4);
MODEL c2:
%c2#1%
[ending2$1@15] (3);
%c2#2%
[ending2$1@-15] (4);
MODEL c3:
%c3#1%
[ending3$1@15] (3);
%c3#2%
[ending3$1@-15] (4);
MODEL c4:
%c4#1%
[ending4$1@15] (3);
%c4#2%
[ending4$1@-15] (4);
OUTPUT:
Appendix C: Mplus syntax for the stationary latent Markov model
TITLE: Latent Markov model for ending letter sounds
homogeneous transition and response probs
Input for analyses reported in lower panel of Table 2
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEV ARE pov ending1 ending2 ending3 ending4;
CATEGORICAL ARE ending1 ending2 ending3 ending4;
classes c1(2) c2(2) c3(2) c4(2)
missing are .;
ANALYSIS:
TYPE = mixture missing;
starts = 100 10;
stiterations = 20;
MODEL:
%OVERALL%
[c1#1-c4#1] (1);
c4#1 ON c3#1 (2);
c3#1 ON c2#1 (2);
c2#1 ON c1#1 (2);
c4#1 ON POV (5);
c3#1 ON POV (5);
c2#1 ON POV (5);
c1#1 ON POV (5);
MODEL c1:
%c1#1%
[ending1$1@2] (3) ;
%c1#2%
[ending1$1@-2] (4);
MODEL c2:
%c2#1%
[ending2$1@2] ;
%c2#2%
[ending2$1@-2] ;
MODEL c3:
%c3#1%
[ending3$1@2] ;
%c3#2%
[ending3$1@-2] ;
MODEL c4:
%c4#1%
[ending4$1@2] (3);
%c4#2%
[ending4$1@-2] (4);
OUTPUT:
Appendix D: Mplus syntax for latent class analysis
TITLE: Latent Class Analysis five reading subtests
Beginning of kindergarten 3-class model
Input for analysis reported in the first column of Table 3
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEV ARE letrec1 begin1 ending1 sight1 wic1;
CLASSES = c(3);
CATEGORICAL ARE letrec1 begin1 ending1 sight1 wic1;
missing are .;
ANALYSIS:
TYPE = MIXTURE missing;
starts = 100 10;
stiterations = 20;
MODEL: %OVERALL%
%c#1%
[letrec1$ begin1$ ending1$ sight1$1@15 wic1$1@15];
%c#2%
[letrec1$ begin1$ ending1$ sight1$ wic1$1@15] ;
%c#3%
[letrec1$1@-15 begin1$ ending1$ sight1$ wic1$ ;
OUTPUT:
Appendix E: Mplus syntax for latent transition analysis assuming
measurement invariance: Total sample
TITLE: Latent transition analysis
Heterogenous transition matrices
3 - class model
Input for analysis reported in Table 4
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEVARIABLES are letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
CATEGORICAL ARE letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
classes = c1(3) c2(3) c3(3) c4(3);
missing are .;
ANALYSIS:
TYPE = mixture missing;
starts = 200 20;
stiterations = 50;
MODEL:
%OVERALL%
[c2#1@-15];
[c2#2@-15];
c2#1 on c1#2@-15;
c2#1 on c1#1;
c2#2 on c1#1;
c2#1 on c1#2;
c2#2 on c1#2;
[c3#1@-15];
[c3#2@-15];
c3#1 on c2#2@-15;
c3#1 on c2#1;
c3#2 on c2#1;
c3#1 on c2#2;
c3#2 on c2#2;
continued
[c4#1@-15];
[c4#2@-15];
c4#1 on c3#2@-15;
c4#1 on c3#1;
c4#2 on c3#1;
c4#1 on c3#2;
c4#2 on c3#2;
MODEL c1:
%c1#1%
[letrec1$ begin1$ ending1$ sight1$1@15 wic1$1@15] ;
%c1#2%
[letrec1$ begin1$ ending1$ sight1$ wic1$1@15] ;
%c1#3%
[letrec1$1@-15 begin1$ ending1$ sight1$ wic1$ ;
MODEL c2:
%c2#1%
[letrec2$ begin2$ ending2$ sight2$1@15 wic2$1@15] ;
%c2#2%
[letrec2$ begin2$ ending2$ sight2$ wic2$1@15] ;
%c2#3%
[letrec2$1@-15 begin2$ ending2$ sight2$ wic2$ ;
MODEL c3:
%c3#1%
[letrec3$ begin3$ ending3$ sight3$1@15 wic3$1@15] ;
%c3#2%
[letrec3$ begin3$ ending3$ sight3$ wic3$1@15] ;
%c3#3%
[letrec3$1@-15 begin3$ ending3$ sight3$ wic3$ ;
MODEL c4:
%c4#1%
[letrec4$ begin4$ ending4$ sight4$1@15 wic4$1@15] ;
%c4#2%
[letrec4$ begin4$ ending4$ sight4$ wic4$1@15] ;
%c4#3%
[letrec4$1@-15 begin4$ ending4$ sight4$ wic4$ ;
OUTPUT:
Appendix F: Mplus syntax for the mover-stayer model: Total sample
TITLE: Mover-Stayer Model
Input for analysis reported in Table 5
DATA: FILE IS C:\analytic.dat;
FORMAT IS f1.0, 20f2.0;
VARIABLE: NAMES ARE pov
letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
USEVARIABLES are letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
CATEGORICAL ARE letrec1 begin1 ending1 sight1 wic1
letrec2 begin2 ending2 sight2 wic2
letrec3 begin3 ending3 sight3 wic3
letrec4 begin4 ending4 sight4 wic4;
classes = c(2) c1(3) c2(3) c3(3) c4(3);
missing are .;
ANALYSIS:
TYPE = mixture missing;
starts = 200 20;
stiterations = 50;
MODEL:
%OVERALL%
c1#1 on c#1;
[c1#1@10];
c2#1 on c#1;
[c2#1@-10];
c3#1 on c#1;
[c3#1@-10];
c4#1 on c#1;
[c4#1@-10];
MODEL c: ! model for movers and stayers
%c#1%
c4#1-c4#2 on c3#1-c3#2 ;
c3#1-c3#2 ON c2#1-c2#2 ;
c2#1-c2#2 ON c1#1-c1#2 ;
%c#2%
c4#1-c4#2 on c3#1-c3#2@20 ;
c3#1-c3#2 ON c2#1-c2#2@20 ;
c2#1-c2#2 ON c1#1-c1#2@20 ;
continued
MODEL c.c1: !mover stayer model for c1
%c#1.c1#1%
[letrec1$1-wic1$1] (1-5) ;
%c#1.c1#2%
[letrec1$1-wic1$1] (6-10);
%c#1.c1#3%
[letrec1$1-wic1$1] (11-15);
%c#2.c1#1%
[letrec1$1-wic1$1@15] ;
%c#2.c1#2%
[letrec1$1-wic1$1@-15] ;
%c#2.c1#3%
[letrec1$1-wic1$1@-15] ;
MODEL c.c2:
%c#1.c2#1%
[letrec2$1-wic2$1] (1-5);
%c#1.c2#2%
[letrec2$1-wic2$1] (6-10);
%c#1.c2#3%
[letrec2$1-wic2$1] (11-15);
%c#2.c2#1%
[letrec2$1-wic2$1@15] ;
%c#2.c2#2%
[letrec2$1-wic2$1@-15] ;
%c#2.c2#3%
[letrec2$1-wic2$1@-15] ;
MODEL c.c3:
%c#1.c3#1%
[letrec3$1-wic3$1] (1-5);
%c#1.c3#2%
[letrec3$1-wic3$1] (6-10);
%c#1.c3#3%
[letrec3$1-wic3$1] (11-15);
%c#2.c3#1%
[letrec3$1- wic3$1@15] ;
%c#2.c3#2%
[letrec3$1-wic3$1@-15] ;
%c#2.c3#3%
[letrec3$1-wic3$1@-15] ;
MODEL c.c4:
%c#1.c4#1%
[letrec4$1-wic4$1] (1-5);
%c#1.c4#2%
[letrec4$1-wic4$1] (6-10);
%c#1.c4#3%
[letrec4$1-wic4$1] (11-15);
%c#2.c4#1%
[letrec4$1-wic4$1@15] ;
%c#2.c4#2%
[letrec4$1-wic4$1@-15] ;
%c#2.c4#3%
[letrec4$1-wic4$1@-15] ;
OUTPUT: