R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

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> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("sem-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('sem')
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "Klein"
> 
> ### * Klein
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Klein
> ### Title: Klein's Data on the U. S. Economy
> ### Aliases: Klein
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(Klein)
> 
> Klein$P.lag <- c(NA, Klein$P[-22])
> Klein$X.lag <- c(NA, Klein$X[-22])
> 
> summary(tsls(C ~ P + P.lag + I(Wp + Wg), 
+     instruments=~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag,
+     data=Klein))

 2SLS Estimates

Model Formula: C ~ P + P.lag + I(Wp + Wg)

Instruments: ~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag

Residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-1.89e+00 -6.16e-01 -2.46e-01  3.10e-11  8.85e-01  2.00e+00 

            Estimate Std. Error t value  Pr(>|t|)
(Intercept) 16.55476    1.46798 11.2772 2.587e-09
P            0.01730    0.13120  0.1319 8.966e-01
P.lag        0.21623    0.11922  1.8137 8.741e-02
I(Wp + Wg)   0.81018    0.04474 18.1107 1.505e-12

Residual standard error: 1.1357 on 17 degrees of freedom

>     
> summary(tsls(I ~ P + P.lag + K.lag,
+     instruments=~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag,
+     data=Klein))

 2SLS Estimates

Model Formula: I ~ P + P.lag + K.lag

Instruments: ~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag

Residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-3.29e+00 -8.07e-01  1.42e-01  3.01e-12  8.60e-01  1.80e+00 

            Estimate Std. Error t value Pr(>|t|)
(Intercept)  20.2782    8.38325  2.4189 0.027071
P             0.1502    0.19253  0.7802 0.445980
P.lag         0.6159    0.18093  3.4044 0.003375
K.lag        -0.1578    0.04015 -3.9298 0.001080

Residual standard error: 1.3071 on 17 degrees of freedom

>     
> summary(tsls(Wp ~ X + X.lag + I(Year - 1931),
+     instruments=~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag,
+     data=Klein))

 2SLS Estimates

Model Formula: Wp ~ X + X.lag + I(Year - 1931)

Instruments: ~1 + G + T + Wg + I(Year - 1931) + K.lag + P.lag + X.lag

Residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-1.29e+00 -4.73e-01  1.45e-02 -3.09e-12  4.49e-01  1.20e+00 

               Estimate Std. Error t value  Pr(>|t|)
(Intercept)      1.5003    1.27569   1.176 2.558e-01
X                0.4389    0.03960  11.082 3.368e-09
X.lag            0.1467    0.04316   3.398 3.422e-03
I(Year - 1931)   0.1304    0.03239   4.026 8.764e-04

Residual standard error: 0.7672 on 17 degrees of freedom

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "Kmenta"
> 
> ### * Kmenta
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Kmenta
> ### Title: Partly Artificial Data on the U. S. Economy
> ### Aliases: Kmenta
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(Kmenta)
> 
> 
> 
> cleanEx(); ..nameEx <- "boot.sem"
> 
> ### * boot.sem
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: boot.sem
> ### Title: Bootstrap a Structural Equation Model
> ### Aliases: boot.sem print.bootsem summary.bootsem
> ### Keywords: htest models
> 
> ### ** Examples
> 
>     ## Not run: 
> ##D 
> ##D # A simple confirmatory factor-analysis model using polychoric correlations.
> ##D #  The polycor package is required for the hetcor function.
> ##D 
> ##D library(polycor)
> ##D 
> ##D # The following function returns correlations computed by hetcor,
> ##D #   and is used for the bootstrapping.
> ##D 
> ##D hcor <- function(data) hetcor(data, std.err=FALSE)$correlations
> ##D 
> ##D model.cnes <- specify.model()
> ##D F -> MBSA2, lam1, NA
> ##D F -> MBSA7, lam2, NA
> ##D F -> MBSA8, lam3, NA
> ##D F -> MBSA9, lam4, NA
> ##D F <-> F, NA, 1
> ##D MBSA2 <-> MBSA2, the1, NA
> ##D MBSA7 <-> MBSA7, the2, NA
> ##D MBSA8 <-> MBSA8, the3, NA
> ##D MBSA9 <-> MBSA9, the4, NA
> ##D 
> ##D data(CNES)
> ##D R.cnes <- hcor(CNES)
> ##D 
> ##D sem.cnes <- sem(model.cnes, R.cnes, N=1529)
> ##D summary(sem.cnes)
> ##D 
> ##D #  Note: this can take a couple of minutes:
> ##D 
> ##D system.time(boot.cnes <- boot.sem(CNES, sem.cnes, R=100, cov=hcor), gcFirst=TRUE)
> ##D summary(boot.cnes, type="norm")  
> ##D # cf., standard errors to those computed by summary(sem.cnes)
> ##D 
> ##D     
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "mod.indices"
> 
> ### * mod.indices
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mod.indices
> ### Title: Modification Indices for Structural Equation Models
> ### Aliases: mod.indices mod.indices.sem print.sem.modind
> ###   summary.sem.modind
> ### Keywords: models
> 
> ### ** Examples
> 
> # This example is adapted from the SAS manual
> 
> S.wh <- matrix(c(
+    11.834,     0,        0,        0,       0,        0,
+     6.947,    9.364,     0,        0,       0,        0,
+     6.819,    5.091,   12.532,     0,       0,        0,
+     4.783,    5.028,    7.495,    9.986,    0,        0,
+    -3.839,   -3.889,   -3.841,   -3.625,   9.610,     0,
+   -21.899,  -18.831,  -21.748,  -18.775,  35.522,  450.288), 
+   6, 6)
> 
> model.wh <- matrix(c(
+                     'Alienation67   ->  Anomia67',      NA,     1,
+                     'Alienation67   ->  Powerless67',   NA,     0.833,
+                     'Alienation71   ->  Anomia71',      NA,     1,
+                     'Alienation71   ->  Powerless71',   NA,     0.833, 
+                     'SES            ->  Education',     NA,     1,     
+                     'SES            ->  SEI',           'lamb', NA,
+                     'SES            ->  Alienation67',  'gam1', NA,
+                     'Alienation67   ->  Alienation71',  'beta', NA,
+                     'SES            ->  Alienation71',  'gam2', NA,
+                     'Anomia67       <-> Anomia67',      'the1', NA,
+                     'Anomia71       <-> Anomia71',      'the1', NA,
+                     'Powerless67    <-> Powerless67',   'the2', NA,
+                     'Powerless71    <-> Powerless71',   'the2', NA,
+                     'Education      <-> Education',     'the3', NA,
+                     'SEI            <-> SEI',           'the4', NA,
+                     'Anomia67       <-> Anomia71',      'the5', NA,
+                     'Powerless67    <-> Powerless71',   'the5', NA,
+                     'Alienation67   <-> Alienation67',  'psi1', NA,
+                     'Alienation71   <-> Alienation71',  'psi2', NA,
+                     'SES            <-> SES',           'phi',  NA), 
+                     ncol=3, byrow=TRUE)
>                                             
> obs.vars.wh <- c('Anomia67','Powerless67','Anomia71','Powerless71','Education','SEI')
> rownames(S.wh) <- colnames(S.wh) <- obs.vars.wh
> 
> sem.wh <- sem(model.wh, S.wh, 932)
> 
> mod.indices(sem.wh)

 5 largest modification indices, A matrix:
Powerless67:Education    Anomia67:Education       Powerless67:SES 
             4.873638              3.802741              2.760836 
Education:Powerless67          Anomia67:SES 
             2.461851              2.312198 

  5 largest modification indices, P matrix:
Education:Powerless67    Education:Anomia67       SES:Powerless67 
             6.402830              4.539805              2.760836 
         SES:Anomia67       SEI:Powerless67 
             2.312198              1.318489 
> 
> ##   5 largest modification indices, A matrix:
> ##  Powerless67:Education    Anomia67:Education 
> ##                 4.8736                3.8027 
> ##        Powerless67:SES Education:Powerless67 
> ##                 2.7608                2.4619 
> ##         Anomia67:SES 
> ##               2.3122 
> ##
> ##    5 largest modification indices, P matrix:
> ##  Education:Powerless67    Education:Anomia67 
> ##                 6.4028                4.5398 
> ##        SES:Powerless67          SES:Anomia67 
> ##                 2.7608                2.3122 
> ##        SEI:Powerless67 
> ##                 1.3185 
> 
> 
> 
> cleanEx(); ..nameEx <- "path.diagram"
> 
> ### * path.diagram
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: path.diagram
> ### Title: Draw Path Diagram
> ### Aliases: path.diagram path.diagram.sem
> ### Keywords: dplot models
> 
> ### ** Examples
> 
> 
> # The Duncan, Haller, and Portes Peer-Influences Model
> 
> R.DHP <- matrix(c(     
+             1,      0,      0,      0,      0,      0,      0,      0,      0,      0,            
+             .6247,   1,     0,      0,      0,      0,      0,      0,      0,      0,            
+             .3269,  .3669,  1,      0,      0,      0,      0,      0,      0,      0,            
+             .4216,  .3275,  .6404,  1,      0,      0,      0,      0,      0,      0,
+             .2137,  .2742,  .1124,  .0839,  1,      0,      0,      0,      0,      0,
+             .4105,  .4043,  .2903,  .2598,  .1839,  1,      0,      0,      0,      0,
+             .3240,  .4047,  .3054,  .2786,  .0489,  .2220,  1,      0,      0,      0,
+             .2930,  .2407,  .4105,  .3607,  .0186,  .1861,  .2707,  1,      0,      0,
+             .2995,  .2863,  .5191,  .5007,  .0782,  .3355,  .2302,  .2950,  1,      0,
+             .0760,  .0702,  .2784,  .1988,  .1147,  .1021,  .0931, -.0438,  .2087,  1
+             ), ncol=10, byrow=TRUE)
> 
> model.dhp <- matrix(c(
+                       'RParAsp  -> RGenAsp', 'gam11',  NA,
+                       'RIQ      -> RGenAsp', 'gam12',  NA,
+                       'RSES     -> RGenAsp', 'gam13',  NA,
+                       'FSES     -> RGenAsp', 'gam14',  NA,
+                       'RSES     -> FGenAsp', 'gam23',  NA,
+                       'FSES     -> FGenAsp', 'gam24',  NA,
+                       'FIQ      -> FGenAsp', 'gam25',  NA,
+                       'FParAsp  -> FGenAsp', 'gam26',  NA,
+                       'FGenAsp  -> RGenAsp', 'beta12', NA,
+                       'RGenAsp  -> FGenAsp', 'beta21', NA,
+                       'RGenAsp  -> ROccAsp',  NA,       1,
+                       'RGenAsp  -> REdAsp',  'lam21',  NA,
+                       'FGenAsp  -> FOccAsp',  NA,       1,
+                       'FGenAsp  -> FEdAsp',  'lam42',  NA,
+                       'RGenAsp <-> RGenAsp', 'ps11',   NA,
+                       'FGenAsp <-> FGenAsp', 'ps22',   NA,
+                       'RGenAsp <-> FGenAsp', 'ps12',   NA,
+                       'ROccAsp <-> ROccAsp', 'theta1', NA,
+                       'REdAsp  <-> REdAsp',  'theta2', NA,
+                       'FOccAsp <-> FOccAsp', 'theta3', NA,
+                       'FEdAsp  <-> FEdAsp',  'theta4', NA),
+                     ncol=3, byrow=TRUE)
> 
> rownames(R.DHP) <- colnames(R.DHP) <- c('ROccAsp', 'REdAsp', 'FOccAsp', 
+     'FEdAsp', 'RParAsp', 'RIQ', 'RSES', 'FSES', 'FIQ', 'FParAsp')
> 
> sem.dhp <- sem(model.dhp, R.DHP, 329,
+     fixed.x=c('RParAsp', 'RIQ', 'RSES', 'FSES', 'FIQ', 'FParAsp'))
>     
> path.diagram(sem.dhp, min.rank='RIQ, RSES, RParAsp, FParAsp, FSES, FIQ', 
+     max.rank='ROccAsp, REdAsp, FEdAsp, FOccAsp')
digraph "sem.dhp" {
  rankdir=LR;
  size="8,8";
  node [fontname="Helvetica" fontsize=14 shape=box];
  edge [fontname="Helvetica" fontsize=10];
  center=1;
  {rank=min "RIQ" "RSES" "RParAsp" "FParAsp" "FSES" "FIQ"}
  {rank=max "ROccAsp" "REdAsp" "FEdAsp" "FOccAsp"}
  "RGenAsp" [shape=ellipse]
  "FGenAsp" [shape=ellipse]
  "RParAsp" -> "RGenAsp" [label="gam11"];
  "RIQ" -> "RGenAsp" [label="gam12"];
  "RSES" -> "RGenAsp" [label="gam13"];
  "FSES" -> "RGenAsp" [label="gam14"];
  "RSES" -> "FGenAsp" [label="gam23"];
  "FSES" -> "FGenAsp" [label="gam24"];
  "FIQ" -> "FGenAsp" [label="gam25"];
  "FParAsp" -> "FGenAsp" [label="gam26"];
  "FGenAsp" -> "RGenAsp" [label="beta12"];
  "RGenAsp" -> "FGenAsp" [label="beta21"];
  "RGenAsp" -> "ROccAsp" [label=""];
  "RGenAsp" -> "REdAsp" [label="lam21"];
  "FGenAsp" -> "FOccAsp" [label=""];
  "FGenAsp" -> "FEdAsp" [label="lam42"];
}
> 
> ##   digraph "sem.dhp" {
> ##   rankdir=LR;
> ##   size="8,8";
> ##   node [fontname="Helvetica" fontsize=14 shape=box];
> ##   edge [fontname="Helvetica" fontsize=10];
> ##   center=1;
> ##   {rank=min "RIQ" "RSES" "RParAsp" "FParAsp" "FSES" "FIQ"}
> ##   {rank=max "ROccAsp" "REdAsp" "FEdAsp" "FOccAsp"}
> ##   "RGenAsp" [shape=ellipse]
> ##   "FGenAsp" [shape=ellipse]
> ##   "RParAsp" -> "RGenAsp" [label="gam11"];
> ##   "RIQ" -> "RGenAsp" [label="gam12"];
> ##   "RSES" -> "RGenAsp" [label="gam13"];
> ##   "FSES" -> "RGenAsp" [label="gam14"];
> ##   "RSES" -> "FGenAsp" [label="gam23"];
> ##   "FSES" -> "FGenAsp" [label="gam24"];
> ##   "FIQ" -> "FGenAsp" [label="gam25"];
> ##   "FParAsp" -> "FGenAsp" [label="gam26"];
> ##   "FGenAsp" -> "RGenAsp" [label="beta12"];
> ##   "RGenAsp" -> "FGenAsp" [label="beta21"];
> ##   "RGenAsp" -> "ROccAsp" [label=""];
> ##   "RGenAsp" -> "REdAsp" [label="lam21"];
> ##   "FGenAsp" -> "FOccAsp" [label=""];
> ##   "FGenAsp" -> "FEdAsp" [label="lam42"];
> ##   }
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "ram"
> 
> ### * ram
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: ram
> ### Title: RAM Matrix for a Structural-Equation Model
> ### Aliases: ram
> ### Keywords: models
> 
> ### ** Examples
> 
> 
> # ------------- assumes that Duncan, Haller and Portes peer-influences model
> # -------------     has been fit and is in sem.dhp
> 
>     ## Not run: 
> ##D ram(sem.dhp)
> ##D 
> ##D ##        heads to from parameter  estimate                arrow
> ##D ##            1  1   11         0  1.000000 ROccAsp <--- RGenAsp
> ##D ## lam21      1  2   11         1  1.062673  REdAsp <--- RGenAsp
> ##D ##            1  3   12         0  1.000000 FOccAsp <--- FGenAsp
> ##D ## lam42      1  4   12         2  0.929732  FEdAsp <--- FGenAsp
> ##D ## gam11      1 11    5         3  0.161220 RGenAsp <--- RParAsp
> ##D ## gam12      1 11    6         4  0.249647     RGenAsp <--- RIQ
> ##D ## gam13      1 11    7         5  0.218402    RGenAsp <--- RSES
> ##D ## gam14      1 11    8         6  0.071836    RGenAsp <--- FSES
> ##D ## gam23      1 12    7         7  0.061879    FGenAsp <--- RSES
> ##D ## gam24      1 12    8         8  0.228863    FGenAsp <--- FSES
> ##D ## gam25      1 12    9         9  0.349030     FGenAsp <--- FIQ
> ##D ## gam26      1 12   10        10  0.159529 FGenAsp <--- FParAsp
> ##D ## beta12     1 11   12        11  0.184245 RGenAsp <--- FGenAsp
> ##D ## beta21     1 12   11        12  0.235502 FGenAsp <--- RGenAsp
> ##D ## theta1     2  1    1        13  0.412143 ROccAsp <--> ROccAsp
> ##D ## theta2     2  2    2        14  0.336146   REdAsp <--> REdAsp
> ##D ## theta3     2  3    3        15  0.311197 FOccAsp <--> FOccAsp
> ##D ## theta4     2  4    4        16  0.404601   FEdAsp <--> FEdAsp
> ##D ## psi11      2 11   11        17  0.280987 RGenAsp <--> RGenAsp
> ##D ## psi22      2 12   12        18  0.263832 FGenAsp <--> FGenAsp
> ##D ## psi12      2 11   12        19 -0.022620 RGenAsp <--> FGenAsp
> ##D ##            2  5    5         0  1.000000 RParAsp <--> RParAsp
> ##D ##            2  6    5         0  0.183900     RIQ <--> RParAsp
> ##D ##            2  6    6         0  1.000000         RIQ <--> RIQ
> ##D ##            2  7    5         0  0.048900    RSES <--> RParAsp
> ##D ##            2  7    6         0  0.222000        RSES <--> RIQ
> ##D ##            2  7    7         0  1.000000       RSES <--> RSES
> ##D ##            2  8    5         0  0.018600    FSES <--> RParAsp
> ##D ##            2  8    6         0  0.186100        FSES <--> RIQ
> ##D ##            2  8    7         0  0.270700       FSES <--> RSES
> ##D ##            2  8    8         0  1.000000       FSES <--> FSES
> ##D ##            2  9    5         0  0.078200     FIQ <--> RParAsp
> ##D ##            2  9    6         0  0.335500         FIQ <--> RIQ
> ##D ##            2  9    7         0  0.230200        FIQ <--> RSES
> ##D ##            2  9    8         0  0.295000        FIQ <--> FSES
> ##D ##            2  9    9         0  1.000000         FIQ <--> FIQ
> ##D ##            2 10    5         0  0.114700 FParAsp <--> RParAsp
> ##D ##            2 10    6         0  0.102100     FParAsp <--> RIQ
> ##D ##            2 10    7         0  0.093100    FParAsp <--> RSES
> ##D ##            2 10    8         0 -0.043800    FParAsp <--> FSES
> ##D ##            2 10    9         0  0.208700     FParAsp <--> FIQ
> ##D ##            2 10   10         0  1.000000 FParAsp <--> FParAsp
> ##D     
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "raw.moments"
> 
> ### * raw.moments
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: raw.moments
> ### Title: Compute Raw Moments Matrix
> ### Aliases: raw.moments raw.moments.formula raw.moments.default
> ###   print.rawmoments
> ### Keywords: manip
> 
> ### ** Examples
> 
> data(Kmenta)
> raw.moments(cbind(1, Kmenta))

Raw Moments
         1          Q          P        D        F        A
1   1.0000   100.8982   100.0191   97.535   96.625   10.500
Q 100.8982 10193.8525 10093.8167 9873.665 9780.155 1062.599
P 100.0191 10093.8167 10037.1729 9793.092 9651.145 1050.194
D  97.5350  9873.6647  9793.0919 9646.039 9494.644 1045.960
F  96.6250  9780.1547  9651.1453 9494.644 9489.828  994.060
A  10.5000  1062.5988  1050.1941 1045.960  994.060  143.500

N =  20 
> raw.moments(~ Q + P + D + F + A, data=Kmenta)

Raw Moments
            (Intercept)          Q          P        D        F        A
(Intercept)      1.0000   100.8982   100.0191   97.535   96.625   10.500
Q              100.8982 10193.8525 10093.8167 9873.665 9780.155 1062.599
P              100.0191 10093.8167 10037.1729 9793.092 9651.145 1050.194
D               97.5350  9873.6647  9793.0919 9646.039 9494.644 1045.960
F               96.6250  9780.1547  9651.1453 9494.644 9489.828  994.060
A               10.5000  1062.5988  1050.1941 1045.960  994.060  143.500

N =  20 
> 
> 
> 
> cleanEx(); ..nameEx <- "residuals"
> 
> ### * residuals
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: residuals.sem
> ### Title: Residual Covariances for a Structural Equation Model
> ### Aliases: residuals.sem standardized.residuals
> ###   standardized.residuals.sem normalized.residuals
> ###   normalized.residuals.sem
> ### Keywords: models
> 
> ### ** Examples
> 
>     ## Not run: 
> ##D # ------------- assumes that Duncan, Haller and Portes peer-influences model
> ##D # -------------     has been fit and is in sem.dhp.1
> ##D 
> ##D residuals(sem.dhp.1)
> ##D 
> ##D ##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
> ##D ##    ROccAsp  4.156103e-07 -2.896368e-07 -2.866110e-02  9.102874e-02
> ##D ##    REdAsp  -2.896368e-07 -1.541581e-06 -1.094841e-02 -2.379215e-02
> ##D ##    FOccAsp -2.866110e-02 -1.094841e-02 -3.740356e-06 -9.564103e-07
> ##D ##    
> ##D ##    . . .
> ##D ##    
> ##D ##                      FIQ       FParAsp
> ##D ##    ROccAsp  3.467853e-02 -3.187309e-02
> ##D ##    REdAsp   4.878970e-03 -4.443480e-02
> ##D ##    FOccAsp -7.354686e-03  2.488120e-02
> ##D ##    FEdAsp   1.124604e-02 -3.690078e-02
> ##D ##    RParAsp  2.775558e-17  5.551115e-17
> ##D ##    RIQ      2.220446e-16  6.938894e-17
> ##D ##    RSES     0.000000e+00 -1.387779e-17
> ##D ##    FSES     1.110223e-16 -2.775558e-17
> ##D ##    FIQ      4.440892e-16  1.110223e-16
> ##D ##    FParAsp  1.110223e-16  4.440892e-16
> ##D 
> ##D normalized.residuals(sem.dhp.1) 
> ##D 
> ##D ##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
> ##D ##    ROccAsp  5.330519e-06 -4.455587e-06 -4.898232e-01  1.567678e+00
> ##D ##    REdAsp  -4.455587e-06 -1.977191e-05 -1.857670e-01 -4.071582e-01
> ##D ##    FOccAsp -4.898232e-01 -1.857670e-01 -4.797271e-05 -1.460881e-05
> ##D ##    
> ##D ##    . . .
> ##D ##    
> ##D ##                      FIQ       FParAsp
> ##D ##    ROccAsp  6.080514e-01 -5.747909e-01
> ##D ##    REdAsp   8.518738e-02 -8.007295e-01
> ##D ##    FOccAsp -1.180429e-01  4.374639e-01
> ##D ##    FEdAsp   1.832159e-01 -6.514685e-01
> ##D ##    RParAsp  5.019082e-16  1.000322e-15
> ##D ##    RIQ      3.818356e-15  1.252092e-15
> ##D ##    RSES     0.000000e+00 -2.506364e-16
> ##D ##    FSES     1.931472e-15 -5.029583e-16
> ##D ##    FIQ      5.695780e-15  1.971289e-15
> ##D ##    FParAsp  1.971289e-15  5.695780e-15
> ##D       
> ##D standardized.residuals(sem.dhp.1)
> ##D 
> ##D ##                  ROccAsp        REdAsp       FOccAsp        FEdAsp
> ##D ##    ROccAsp  4.156103e-07 -2.896368e-07 -2.866110e-02  9.102874e-02
> ##D ##    REdAsp  -2.896368e-07 -1.541581e-06 -1.094841e-02 -2.379215e-02
> ##D ##    FOccAsp -2.866110e-02 -1.094841e-02 -3.740356e-06 -9.564103e-07
> ##D ##    
> ##D ##    . . .
> ##D ##    
> ##D ##                      FIQ       FParAsp
> ##D ##    ROccAsp  3.467853e-02 -3.187309e-02
> ##D ##    REdAsp   4.878970e-03 -4.443480e-02
> ##D ##    FOccAsp -7.354686e-03  2.488120e-02
> ##D ##    FEdAsp   1.124604e-02 -3.690078e-02
> ##D ##    RParAsp  2.775558e-17  5.551115e-17
> ##D ##    RIQ      2.220446e-16  6.938894e-17
> ##D ##    RSES     0.000000e+00 -1.387779e-17
> ##D ##    FSES     1.110223e-16 -2.775558e-17
> ##D ##    FIQ      4.440892e-16  1.110223e-16
> ##D ##    FParAsp  1.110223e-16  4.440892e-16
> ##D     
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "sem"
> 
> ### * sem
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sem
> ### Title: General Structural Equation Models
> ### Aliases: sem sem.mod sem.default startvalues print.sem summary.sem
> ###   print.summary.sem
> ### Keywords: models
> 
> ### ** Examples
> 
> 
> # ------------- Duncan, Haller and Portes peer-influences model ----------------------
> # A nonrecursive SEM with unobserved endogenous variables and fixed exogenous variables
> 
> R.DHP <- matrix(c(      # lower triangle of correlation matrix
+             1,      0,      0,      0,      0,      0,      0,      0,      0,      0,            
+             .6247,   1,     0,      0,      0,      0,      0,      0,      0,      0,            
+             .3269,  .3669,  1,      0,      0,      0,      0,      0,      0,      0,            
+             .4216,  .3275,  .6404,  1,      0,      0,      0,      0,      0,      0,
+             .2137,  .2742,  .1124,  .0839,  1,      0,      0,      0,      0,      0,
+             .4105,  .4043,  .2903,  .2598,  .1839,  1,      0,      0,      0,      0,
+             .3240,  .4047,  .3054,  .2786,  .0489,  .2220,  1,      0,      0,      0,
+             .2930,  .2407,  .4105,  .3607,  .0186,  .1861,  .2707,  1,      0,      0,
+             .2995,  .2863,  .5191,  .5007,  .0782,  .3355,  .2302,  .2950,  1,      0,
+             .0760,  .0702,  .2784,  .1988,  .1147,  .1021,  .0931, -.0438,  .2087,  1
+             ), ncol=10, byrow=TRUE)
> 
> # Fit the model using a symbolic ram specification
> 
> model.dhp <- specify.model()
1:     RParAsp  -> RGenAsp, gam11,  NA
2:     RIQ      -> RGenAsp, gam12,  NA
3:     RSES     -> RGenAsp, gam13,  NA
4:     FSES     -> RGenAsp, gam14,  NA
5:     RSES     -> FGenAsp, gam23,  NA
6:     FSES     -> FGenAsp, gam24,  NA
7:     FIQ      -> FGenAsp, gam25,  NA
8:     FParAsp  -> FGenAsp, gam26,  NA
9:     FGenAsp  -> RGenAsp, beta12, NA
10:     RGenAsp  -> FGenAsp, beta21, NA
11:     RGenAsp  -> ROccAsp,  NA,     1
12:     RGenAsp  -> REdAsp,  lam21,  NA
13:     FGenAsp  -> FOccAsp,  NA,     1
14:     FGenAsp  -> FEdAsp,  lam42,  NA
15:     RGenAsp <-> RGenAsp, ps11,   NA
16:     FGenAsp <-> FGenAsp, ps22,   NA
17:     RGenAsp <-> FGenAsp, ps12,   NA
18:     ROccAsp <-> ROccAsp, theta1, NA
19:     REdAsp  <-> REdAsp,  theta2, NA
20:     FOccAsp <-> FOccAsp, theta3, NA
21:     FEdAsp  <-> FEdAsp,  theta4, NA
22: 
Read 21 records
> obs.vars.dhp <- c('ROccAsp', 'REdAsp', 'FOccAsp', 'FEdAsp', 'RParAsp', 'RIQ',
+                 'RSES', 'FSES', 'FIQ', 'FParAsp')
> 
> sem.dhp.1 <- sem(model.dhp, R.DHP, 329, obs.vars.dhp, 
+     fixed.x=c('RParAsp', 'RIQ', 'RSES', 'FSES', 'FIQ', 'FParAsp'))
> 
> summary(sem.dhp.1)

 Model Chisquare =  26.697   Df =  15 Pr(>Chisq) = 0.031302
 Goodness-of-fit index =  0.98439
 Adjusted goodness-of-fit index =  0.94275
 RMSEA index =  0.048759   90 % CI: (0.014517, 0.07831)
 BIC =  -94.782 

 Normalized Residuals
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-0.7990 -0.1180  0.0000 -0.0120  0.0397  1.5700 

 Parameter Estimates
       Estimate  Std Error z value Pr(>|z|)                       
gam11   0.161224 0.038487   4.1890 2.8019e-05 RGenAsp <--- RParAsp
gam12   0.249653 0.044580   5.6001 2.1428e-08 RGenAsp <--- RIQ    
gam13   0.218404 0.043476   5.0235 5.0730e-07 RGenAsp <--- RSES   
gam14   0.071843 0.050335   1.4273 1.5350e-01 RGenAsp <--- FSES   
gam23   0.061894 0.051738   1.1963 2.3158e-01 FGenAsp <--- RSES   
gam24   0.228868 0.044495   5.1437 2.6938e-07 FGenAsp <--- FSES   
gam25   0.349039 0.044551   7.8346 4.6629e-15 FGenAsp <--- FIQ    
gam26   0.159535 0.040129   3.9755 7.0224e-05 FGenAsp <--- FParAsp
beta12  0.184226 0.096207   1.9149 5.5506e-02 RGenAsp <--- FGenAsp
beta21  0.235458 0.119742   1.9664 4.9255e-02 FGenAsp <--- RGenAsp
lam21   1.062674 0.091967  11.5549 0.0000e+00 REdAsp <--- RGenAsp 
lam42   0.929727 0.071152  13.0668 0.0000e+00 FEdAsp <--- FGenAsp 
ps11    0.280987 0.046311   6.0674 1.2999e-09 RGenAsp <--> RGenAsp
ps22    0.263836 0.044902   5.8759 4.2067e-09 FGenAsp <--> FGenAsp
ps12   -0.022601 0.051649  -0.4376 6.6168e-01 FGenAsp <--> RGenAsp
theta1  0.412145 0.052211   7.8939 2.8866e-15 ROccAsp <--> ROccAsp
theta2  0.336148 0.053323   6.3040 2.9003e-10 REdAsp <--> REdAsp  
theta3  0.311194 0.046665   6.6687 2.5800e-11 FOccAsp <--> FOccAsp
theta4  0.404604 0.046733   8.6578 0.0000e+00 FEdAsp <--> FEdAsp  

 Iterations =  28 
> 
> ##  Model Chisquare =  26.697   Df =  15 Pr(>Chisq) = 0.031302
> ##  Goodness-of-fit index =  0.98439
> ##  Adjusted goodness-of-fit index =  0.94275
> ##  RMSEA index =  0.048759   90 
> ##  BIC =  -94.782 
> ## 
> ##  Normalized Residuals
> ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
> ## -0.8010 -0.1180  0.0000 -0.0120  0.0398  1.5700 
> ## 
> ##  Parameter Estimates
> ##        Estimate  Std Error z value Pr(>|z|)                       
> ## gam11   0.161224 0.038487   4.1890 2.8019e-05 RGenAsp <--- RParAsp
> ## gam12   0.249653 0.044580   5.6001 2.1428e-08 RGenAsp <--- RIQ    
> ## gam13   0.218404 0.043476   5.0235 5.0730e-07 RGenAsp <--- RSES   
> ## gam14   0.071843 0.050335   1.4273 1.5350e-01 RGenAsp <--- FSES   
> ## gam23   0.061894 0.051738   1.1963 2.3158e-01 FGenAsp <--- RSES   
> ## gam24   0.228868 0.044495   5.1437 2.6938e-07 FGenAsp <--- FSES   
> ## gam25   0.349039 0.044551   7.8346 4.6629e-15 FGenAsp <--- FIQ    
> ## gam26   0.159535 0.040129   3.9755 7.0224e-05 FGenAsp <--- FParAsp
> ## beta12  0.184226 0.096207   1.9149 5.5506e-02 RGenAsp <--- FGenAsp
> ## beta21  0.235458 0.119742   1.9664 4.9255e-02 FGenAsp <--- RGenAsp
> ## lam21   1.062674 0.091967  11.5549 0.0000e+00 REdAsp <--- RGenAsp 
> ## lam42   0.929727 0.071152  13.0668 0.0000e+00 FEdAsp <--- FGenAsp 
> ## ps11    0.280987 0.046311   6.0674 1.2999e-09 RGenAsp <--> RGenAsp
> ## ps22    0.263836 0.044902   5.8759 4.2068e-09 FGenAsp <--> FGenAsp
> ## ps12   -0.022601 0.051649  -0.4376 6.6168e-01 FGenAsp <--> RGenAsp
> ## theta1  0.412145 0.052211   7.8939 2.8866e-15 ROccAsp <--> ROccAsp
> ## theta2  0.336148 0.053323   6.3040 2.9003e-10 REdAsp <--> REdAsp  
> ## theta3  0.311194 0.046665   6.6687 2.5800e-11 FOccAsp <--> FOccAsp
> ## theta4  0.404604 0.046733   8.6578 0.0000e+00 FEdAsp <--> FEdAsp  
> ##
> ##  Iterations =  28 
> 
> ## Not run: 
> ##D 
> ##D # Fit the model using a numerical ram specification
> ##D 
> ##D ram.dhp <- matrix(c(
> ##D #               heads   to      from    param  start
> ##D                 1,       1,     11,      0,     1,
> ##D                 1,       2,     11,      1,     NA, # lam21
> ##D                 1,       3,     12,      0,     1,
> ##D                 1,       4,     12,      2,     NA, # lam42
> ##D                 1,      11,      5,      3,     NA, # gam11
> ##D                 1,      11,      6,      4,     NA, # gam12
> ##D                 1,      11,      7,      5,     NA, # gam13
> ##D                 1,      11,      8,      6,     NA, # gam14
> ##D                 1,      12,      7,      7,     NA, # gam23
> ##D                 1,      12,      8,      8,     NA, # gam24
> ##D                 1,      12,      9,      9,     NA, # gam25
> ##D                 1,      12,     10,     10,     NA, # gam26
> ##D                 1,      11,     12,     11,     NA, # beta12
> ##D                 1,      12,     11,     12,     NA, # beta21
> ##D                 2,       1,      1,     13,     NA, # theta1
> ##D                 2,       2,      2,     14,     NA, # theta2
> ##D                 2,       3,      3,     15,     NA, # theta3
> ##D                 2,       4,      4,     16,     NA, # theta4
> ##D                 2,      11,     11,     17,     NA, # psi11
> ##D                 2,      12,     12,     18,     NA, # psi22
> ##D                 2,      11,     12,     19,     NA  # psi12
> ##D                 ), ncol=5, byrow=TRUE)
> ##D 
> ##D params.dhp <- c('lam21', 'lam42', 'gam11', 'gam12', 'gam13', 'gam14',
> ##D                  'gam23',  'gam24',  'gam25',  'gam26',
> ##D                  'beta12', 'beta21', 'theta1', 'theta2', 'theta3', 'theta4',
> ##D                  'psi11', 'psi22', 'psi12')
> ##D                  
> ##D vars.dhp <- c('ROccAsp', 'REdAsp', 'FOccAsp', 'FEdAsp', 'RParAsp', 'RIQ',
> ##D                 'RSES', 'FSES', 'FIQ', 'FParAsp', 'RGenAsp', 'FGenAsp')
> ##D                 
> ##D sem.dhp.2 <- sem(ram.dhp, R.DHP, 329, params.dhp, vars.dhp, fixed.x=5:10)
> ##D 
> ##D summary(sem.dhp.2)
> ##D     
> ##D ##  Model Chisquare =  26.697   Df =  15 Pr(>Chisq) = 0.031302
> ##D ##  Goodness-of-fit index =  0.98439
> ##D ##  Adjusted goodness-of-fit index =  0.94275
> ##D ##  RMSEA index =  0.048759   90 
> ##D ##  BIC =  -94.782 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
> ##D ## -0.8010 -0.1180  0.0000 -0.0120  0.0398  1.5700 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##        Estimate  Std Error z value Pr(>|z|)                       
> ##D ## lam21   1.062674 0.091967  11.5549 0.0000e+00 REdAsp <--- RGenAsp 
> ##D ## lam42   0.929727 0.071152  13.0668 0.0000e+00 FEdAsp <--- FGenAsp 
> ##D ## gam11   0.161224 0.038487   4.1890 2.8019e-05 RGenAsp <--- RParAsp
> ##D ## gam12   0.249653 0.044580   5.6001 2.1428e-08 RGenAsp <--- RIQ    
> ##D ## gam13   0.218404 0.043476   5.0235 5.0730e-07 RGenAsp <--- RSES   
> ##D ## gam14   0.071843 0.050335   1.4273 1.5350e-01 RGenAsp <--- FSES   
> ##D ## gam23   0.061894 0.051738   1.1963 2.3158e-01 FGenAsp <--- RSES   
> ##D ## gam24   0.228868 0.044495   5.1437 2.6938e-07 FGenAsp <--- FSES   
> ##D ## gam25   0.349039 0.044551   7.8346 4.6629e-15 FGenAsp <--- FIQ    
> ##D ## gam26   0.159535 0.040129   3.9755 7.0224e-05 FGenAsp <--- FParAsp
> ##D ## beta12  0.184226 0.096207   1.9149 5.5506e-02 RGenAsp <--- FGenAsp
> ##D ## beta21  0.235458 0.119742   1.9664 4.9255e-02 FGenAsp <--- RGenAsp
> ##D ## theta1  0.412145 0.052211   7.8939 2.8866e-15 ROccAsp <--> ROccAsp
> ##D ## theta2  0.336148 0.053323   6.3040 2.9003e-10 REdAsp <--> REdAsp  
> ##D ## theta3  0.311194 0.046665   6.6687 2.5800e-11 FOccAsp <--> FOccAsp
> ##D ## theta4  0.404604 0.046733   8.6578 0.0000e+00 FEdAsp <--> FEdAsp  
> ##D ## psi11   0.280987 0.046311   6.0674 1.2999e-09 RGenAsp <--> RGenAsp
> ##D ## psi22   0.263836 0.044902   5.8759 4.2067e-09 FGenAsp <--> FGenAsp
> ##D ## psi12  -0.022601 0.051649  -0.4376 6.6168e-01 RGenAsp <--> FGenAsp
> ##D ##
> ##D ##  Iterations =  28 
> ##D 
> ##D # -------------------- Wheaton et al. alienation data ----------------------
> ##D     
> ##D 
> ##D S.wh <- matrix(c(
> ##D    11.834,     0,        0,        0,       0,        0,
> ##D     6.947,    9.364,     0,        0,       0,        0,
> ##D     6.819,    5.091,   12.532,     0,       0,        0,
> ##D     4.783,    5.028,    7.495,    9.986,    0,        0,
> ##D    -3.839,   -3.889,   -3.841,   -3.625,   9.610,     0,
> ##D   -21.899,  -18.831,  -21.748,  -18.775,  35.522,  450.288), 
> ##D   6, 6)
> ##D   
> ##D # This is the model in the SAS manual for PROC CALIS: A Recursive SEM with
> ##D # latent endogenous and exogenous variables.
> ##D # Curiously, both factor loadings for two of the latent variables are fixed.
> ##D 
> ##D model.wh.1 <- specify.model()
> ##D     Alienation67   ->  Anomia67,      NA,     1
> ##D     Alienation67   ->  Powerless67,   NA,     0.833
> ##D     Alienation71   ->  Anomia71,      NA,     1
> ##D     Alienation71   ->  Powerless71,   NA,     0.833 
> ##D     SES            ->  Education,     NA,     1     
> ##D     SES            ->  SEI,           lamb,   NA
> ##D     SES            ->  Alienation67,  gam1,   NA
> ##D     Alienation67   ->  Alienation71,  beta,   NA
> ##D     SES            ->  Alienation71,  gam2,   NA
> ##D     Anomia67       <-> Anomia67,      the1,   NA
> ##D     Anomia71       <-> Anomia71,      the1,   NA
> ##D     Powerless67    <-> Powerless67,   the2,   NA
> ##D     Powerless71    <-> Powerless71,   the2,   NA
> ##D     Education      <-> Education,     the3,   NA
> ##D     SEI            <-> SEI,           the4,   NA
> ##D     Anomia67       <-> Anomia71,      the5,   NA
> ##D     Powerless67    <-> Powerless71,   the5,   NA
> ##D     Alienation67   <-> Alienation67,  psi1,   NA
> ##D     Alienation71   <-> Alienation71,  psi2,   NA
> ##D     SES            <-> SES,           phi,    NA
> ##D     
> ##D                         
> ##D obs.vars.wh <- c('Anomia67','Powerless67','Anomia71','Powerless71','Education','SEI')
> ##D 
> ##D sem.wh.1 <- sem(model.wh.1, S.wh, 932, obs.vars.wh)
> ##D 
> ##D summary(sem.wh.1)
> ##D 
> ##D ##  Model Chisquare =  13.485   Df =  9 Pr(>Chisq) = 0.14186
> ##D ##  Goodness-of-fit index =  0.99527
> ##D ##  Adjusted goodness-of-fit index =  0.98896
> ##D ##  RMSEA index =  0.023136   90 
> ##D ##  BIC =  -64.177 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
> ##D ## -1.26000 -0.13100  0.00014 -0.02870  0.11400  0.87500 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##      Estimate  Std Error z value  Pr(>|z|)                                 
> ##D ## lamb   5.36880  0.433981  12.3710 0.0000e+00 SEI <--- SES                  
> ##D ## gam1  -0.62994  0.056128 -11.2234 0.0000e+00 Alienation67 <--- SES         
> ##D ## beta   0.59312  0.046820  12.6680 0.0000e+00 Alienation71 <--- Alienation67
> ##D ## gam2  -0.24086  0.055202  -4.3632 1.2817e-05 Alienation71 <--- SES         
> ##D ## the1   3.60787  0.200589  17.9864 0.0000e+00 Anomia67 <--> Anomia67        
> ##D ## the2   3.59494  0.165234  21.7567 0.0000e+00 Powerless67 <--> Powerless67  
> ##D ## the3   2.99366  0.498971   5.9997 1.9772e-09 Education <--> Education      
> ##D ## the4 259.57583 18.321099  14.1681 0.0000e+00 SEI <--> SEI                  
> ##D ## the5   0.90579  0.121711   7.4422 9.9032e-14 Anomia71 <--> Anomia67        
> ##D ## psi1   5.67050  0.422906  13.4084 0.0000e+00 Alienation67 <--> Alienation67
> ##D ## psi2   4.51481  0.334993  13.4773 0.0000e+00 Alienation71 <--> Alienation71
> ##D ## phi    6.61632  0.639506  10.3460 0.0000e+00 SES <--> SES                  
> ##D ##
> ##D ##  Iterations =  78 
> ##D 
> ##D # The same model, but treating one loading for each latent variable as free.
> ##D 
> ##D model.wh.2 <- specify.model()
> ##D     Alienation67   ->  Anomia67,      NA,        1
> ##D     Alienation67   ->  Powerless67,   lamby,    NA
> ##D     Alienation71   ->  Anomia71,      NA,        1
> ##D     Alienation71   ->  Powerless71,   lamby,    NA 
> ##D     SES            ->  Education,     NA,        1     
> ##D     SES            ->  SEI,           lambx,    NA
> ##D     SES            ->  Alienation67,  gam1,     NA
> ##D     Alienation67   ->  Alienation71,  beta,     NA
> ##D     SES            ->  Alienation71,  gam2,     NA
> ##D     Anomia67       <-> Anomia67,      the1,     NA
> ##D     Anomia71       <-> Anomia71,      the1,     NA
> ##D     Powerless67    <-> Powerless67,   the2,     NA
> ##D     Powerless71    <-> Powerless71,   the2,     NA
> ##D     Education      <-> Education,     the3,     NA
> ##D     SEI            <-> SEI,           the4,     NA
> ##D     Anomia67       <-> Anomia71,      the5,     NA
> ##D     Powerless67    <-> Powerless71,   the5,     NA
> ##D     Alienation67   <-> Alienation67,  psi1,     NA
> ##D     Alienation71   <-> Alienation71,  psi2,     NA
> ##D     SES            <-> SES,           phi,      NA 
> ##D 
> ##D sem.wh.2 <- sem(model.wh.2, S.wh, 932, obs.vars.wh)
> ##D 
> ##D summary(sem.wh.2)
> ##D 
> ##D ##  Model Chisquare =  12.673   Df =  8 Pr(>Chisq) = 0.12360
> ##D ##  Goodness-of-fit index =  0.99553
> ##D ##  Adjusted goodness-of-fit index =  0.98828
> ##D ##  RMSEA index =  0.025049   90 
> ##D ##  BIC =  -56.36 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> ##D ## -0.998000 -0.140000  0.000296 -0.028800  0.100000  0.759000 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##       Estimate  Std Error z value  Pr(>|z|)                                 
> ##D ## lamby   0.86261  0.033383  25.8402 0.0000e+00 Powerless67 <--- Alienation67 
> ##D ## lambx   5.35302  0.432591  12.3743 0.0000e+00 SEI <--- SES                  
> ##D ## gam1   -0.62129  0.056142 -11.0663 0.0000e+00 Alienation67 <--- SES         
> ##D ## beta    0.59428  0.047040  12.6335 0.0000e+00 Alienation71 <--- Alienation67
> ##D ## gam2   -0.23580  0.054684  -4.3121 1.6173e-05 Alienation71 <--- SES         
> ##D ## the1    3.74499  0.249823  14.9906 0.0000e+00 Anomia67 <--> Anomia67        
> ##D ## the2    3.49378  0.200754  17.4033 0.0000e+00 Powerless67 <--> Powerless67  
> ##D ## the3    2.97409  0.499662   5.9522 2.6457e-09 Education <--> Education      
> ##D ## the4  260.13252 18.298143  14.2163 0.0000e+00 SEI <--> SEI                  
> ##D ## the5    0.90377  0.121818   7.4190 1.1791e-13 Anomia71 <--> Anomia67        
> ##D ## psi1    5.47380  0.464074  11.7951 0.0000e+00 Alienation67 <--> Alienation67
> ##D ## psi2    4.36410  0.362722  12.0315 0.0000e+00 Alienation71 <--> Alienation71
> ##D ## phi     6.63576  0.640425  10.3615 0.0000e+00 SES <--> SES                  
> ##D ##
> ##D ##  Iterations =  79 
> ##D 
> ##D # ----------------------- Thurstone data ---------------------------------------
> ##D #  Second-order confirmatory factor analysis, from the SAS manual for PROC CALIS
> ##D 
> ##D R.thur <- matrix(c(
> ##D         1.,       0,      0,      0,      0,      0,      0,      0,      0, 
> ##D          .828,   1.,      0,      0,      0,      0,      0,      0,      0, 
> ##D          .776,   .779,   1.,      0,      0,      0,      0,      0,      0, 
> ##D          .439,   .493,    .460,   1.,     0,      0,      0,      0,      0, 
> ##D          .432,   .464,    .425,   .674,   1.,     0,      0,      0,      0, 
> ##D          .447,   .489,    .443,   .590,    .541,  1.,     0,      0,      0, 
> ##D          .447,   .432,    .401,   .381,    .402,   .288,  1.,     0,      0, 
> ##D          .541,   .537,    .534,   .350,    .367,   .320,   .555,  1.,     0, 
> ##D          .380,   .358,    .359,   .424,    .446,   .325,   .598,   .452,  1.
> ##D             ), ncol=9, byrow=TRUE)
> ##D 
> ##D model.thur <- specify.model()
> ##D     F1 -> Sentences,                      lam11, NA
> ##D     F1 -> Vocabulary,                     lam21, NA
> ##D     F1 -> Sent.Completion,                lam31, NA
> ##D     F2 -> First.Letters,                  lam41, NA
> ##D     F2 -> 4.Letter.Words,                 lam52, NA
> ##D     F2 -> Suffixes,                       lam62, NA
> ##D     F3 -> Letter.Series,                  lam73, NA
> ##D     F3 -> Pedigrees,                      lam83, NA
> ##D     F3 -> Letter.Group,                   lam93, NA
> ##D     F4 -> F1,                             gam1,  NA
> ##D     F4 -> F2,                             gam2,  NA
> ##D     F4 -> F3,                             gam3,  NA 
> ##D     Sentences <-> Sentences,              th1,   NA
> ##D     Vocabulary <-> Vocabulary,            th2,   NA
> ##D     Sent.Completion <-> Sent.Completion,  th3,   NA
> ##D     First.Letters <-> First.Letters,      th4,   NA
> ##D     4.Letter.Words <-> 4.Letter.Words,    th5,   NA
> ##D     Suffixes <-> Suffixes,                th6,   NA
> ##D     Letter.Series <-> Letter.Series,      th7,   NA
> ##D     Pedigrees <-> Pedigrees,              th8,   NA
> ##D     Letter.Group <-> Letter.Group,        th9,   NA
> ##D     F1 <-> F1,                            NA,     1
> ##D     F2 <-> F2,                            NA,     1
> ##D     F3 <-> F3,                            NA,     1
> ##D     F4 <-> F4,                            NA,     1
> ##D 
> ##D                         
> ##D obs.vars.thur <- c('Sentences','Vocabulary','Sent.Completion','First.Letters',
> ##D                 '4.Letter.Words','Suffixes','Letter.Series','Pedigrees',
> ##D                 'Letter.Group')
> ##D 
> ##D sem.thur <- sem(model.thur, R.thur, 213, obs.vars.thur)
> ##D 
> ##D summary(sem.thur)
> ##D 
> ##D ##  Model Chisquare =  38.196   Df =  24 Pr(>Chisq) = 0.033101
> ##D ##  Goodness-of-fit index =  0.95957
> ##D ##  Adjusted goodness-of-fit index =  0.9242
> ##D ##  RMSEA index =  0.052822   90 
> ##D ##  BIC =  -143.21 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> ##D ## -9.75e-01 -4.17e-01 -2.90e-06  4.02e-02  9.41e-02  1.63e+00 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##       Estimate Std Error z value Pr(>|z|)                                       
> ##D ## lam11 0.51512  0.064964  7.9293  2.2204e-15 Sentences <--- F1                   
> ##D ## lam21 0.52031  0.065162  7.9849  1.3323e-15 Vocabulary <--- F1                  
> ##D ## lam31 0.48743  0.062422  7.8087  5.7732e-15 Sent.Completion <--- F1             
> ##D ## lam41 0.52112  0.063137  8.2538  2.2204e-16 First.Letters <--- F2               
> ##D ## lam52 0.49707  0.059673  8.3298  0.0000e+00 4.Letter.Words <--- F2              
> ##D ## lam62 0.43806  0.056479  7.7562  8.6597e-15 Suffixes <--- F2                    
> ##D ## lam73 0.45244  0.071372  6.3392  2.3103e-10 Letter.Series <--- F3               
> ##D ## lam83 0.41729  0.061037  6.8367  8.1031e-12 Pedigrees <--- F3                   
> ##D ## lam93 0.40763  0.064524  6.3175  2.6587e-10 Letter.Group <--- F3                
> ##D ## gam1  1.44381  0.264173  5.4654  4.6186e-08 F1 <--- F4                          
> ##D ## gam2  1.25383  0.216597  5.7888  7.0904e-09 F2 <--- F4                          
> ##D ## gam3  1.40655  0.279332  5.0354  4.7684e-07 F3 <--- F4                          
> ##D ## th1   0.18150  0.028401  6.3907  1.6517e-10 Sentences <--> Sentences            
> ##D ## th2   0.16493  0.027797  5.9334  2.9679e-09 Vocabulary <--> Vocabulary          
> ##D ## th3   0.26713  0.033469  7.9816  1.5543e-15 Sent.Completion <--> Sent.Completion
> ##D ## th4   0.30150  0.050686  5.9484  2.7074e-09 First.Letters <--> First.Letters    
> ##D ## th5   0.36450  0.052358  6.9617  3.3618e-12 4.Letter.Words <--> 4.Letter.Words  
> ##D ## th6   0.50641  0.059963  8.4455  0.0000e+00 Suffixes <--> Suffixes              
> ##D ## th7   0.39033  0.061599  6.3367  2.3474e-10 Letter.Series <--> Letter.Series    
> ##D ## th8   0.48137  0.065388  7.3618  1.8141e-13 Pedigrees <--> Pedigrees            
> ##D ## th9   0.50510  0.065227  7.7437  9.5479e-15 Letter.Group <--> Letter.Group      
> ##D ##
> ##D ##  Iterations =  53 
> ##D 
> ##D #------------------------- Kerchoff/Kenney path analysis ---------------------
> ##D # An observed-variable recursive SEM from the LISREL manual
> ##D 
> ##D R.kerch <- matrix(c(
> ##D     1,      0,      0,      0,      0,      0,      0,
> ##D     -.100,  1,      0,      0,      0,      0,      0,
> ##D      .277,  -.152,  1,      0,      0,      0,      0,
> ##D      .250,  -.108,  .611,   1,      0,      0,      0,
> ##D      .572,  -.105,  .294,   .248,   1,      0,      0,
> ##D      .489,  -.213,  .446,   .410,   .597,   1,      0,
> ##D      .335,  -.153,  .303,   .331,   .478,   .651,   1),
> ##D      ncol=7, byrow=TRUE)
> ##D 
> ##D rownames(R.kerch) <- colnames(R.kerch) <- c('Intelligence','Siblings',
> ##D     'FatherEd','FatherOcc','Grades','EducExp','OccupAsp')
> ##D 
> ##D     
> ##D model.kerch <- specify.model()
> ##D     Intelligence -> Grades,       gam51,    NA
> ##D     Siblings -> Grades,           gam52,    NA
> ##D     FatherEd -> Grades,           gam53,    NA
> ##D     FatherOcc -> Grades,          gam54,    NA
> ##D     Intelligence -> EducExp,      gam61,    NA
> ##D     Siblings -> EducExp,          gam62,    NA
> ##D     FatherEd -> EducExp,          gam63,    NA
> ##D     FatherOcc -> EducExp,         gam64,    NA
> ##D     Grades -> EducExp,            beta65,   NA
> ##D     Intelligence -> OccupAsp,     gam71,    NA
> ##D     Siblings -> OccupAsp,         gam72,    NA
> ##D     FatherEd -> OccupAsp,         gam73,    NA
> ##D     FatherOcc -> OccupAsp,        gam74,    NA
> ##D     Grades -> OccupAsp,           beta75,   NA
> ##D     EducExp -> OccupAsp,          beta76,   NA
> ##D     Grades <-> Grades,            psi5,     NA
> ##D     EducExp <-> EducExp,          psi6,     NA
> ##D     OccupAsp <-> OccupAsp,        psi7,     NA
> ##D 
> ##D                        
> ##D sem.kerch <- sem(model.kerch, R.kerch, 737, fixed.x=c('Intelligence','Siblings',
> ##D     'FatherEd','FatherOcc'))
> ##D     
> ##D summary(sem.kerch)
> ##D 
> ##D ##  Model Chisquare =  3.2685e-13   Df =  0 Pr(>Chisq) = NA
> ##D ##  Goodness-of-fit index =  1
> ##D ##  Adjusted goodness-of-fit index =  NA
> ##D ##  RMSEA index =  Inf   90 
> ##D ##  BIC =  NA 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> ##D ## -4.26e-15 -1.35e-15  0.00e+00 -4.17e-16  0.00e+00  1.49e-15 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##        Estimate  Std Error z value  Pr(>|z|)                             
> ##D ## gam51   0.525902 0.031182  16.86530 0.0000e+00 Grades <--- Intelligence  
> ##D ## gam52  -0.029942 0.030149  -0.99314 3.2064e-01 Grades <--- Siblings      
> ##D ## gam53   0.118966 0.038259   3.10951 1.8740e-03 Grades <--- FatherEd      
> ##D ## gam54   0.040603 0.037785   1.07456 2.8257e-01 Grades <--- FatherOcc     
> ##D ## gam61   0.160270 0.032710   4.89979 9.5940e-07 EducExp <--- Intelligence 
> ##D ## gam62  -0.111779 0.026876  -4.15899 3.1966e-05 EducExp <--- Siblings     
> ##D ## gam63   0.172719 0.034306   5.03461 4.7881e-07 EducExp <--- FatherEd     
> ##D ## gam64   0.151852 0.033688   4.50758 6.5571e-06 EducExp <--- FatherOcc    
> ##D ## beta65  0.405150 0.032838  12.33799 0.0000e+00 EducExp <--- Grades       
> ##D ## gam71  -0.039405 0.034500  -1.14215 2.5339e-01 OccupAsp <--- Intelligence
> ##D ## gam72  -0.018825 0.028222  -0.66700 5.0477e-01 OccupAsp <--- Siblings    
> ##D ## gam73  -0.041333 0.036216  -1.14126 2.5376e-01 OccupAsp <--- FatherEd    
> ##D ## gam74   0.099577 0.035446   2.80924 4.9658e-03 OccupAsp <--- FatherOcc   
> ##D ## beta75  0.157912 0.037443   4.21738 2.4716e-05 OccupAsp <--- Grades      
> ##D ## beta76  0.549593 0.038260  14.36486 0.0000e+00 OccupAsp <--- EducExp     
> ##D ## psi5    0.650995 0.033946  19.17743 0.0000e+00 Grades <--> Grades        
> ##D ## psi6    0.516652 0.026943  19.17590 0.0000e+00 EducExp <--> EducExp      
> ##D ## psi7    0.556617 0.029026  19.17644 0.0000e+00 OccupAsp <--> OccupAsp    
> ##D ##
> ##D ##  Iterations =  0 
> ##D 
> ##D #------------------- McArdle/Epstein latent-growth-curve model -----------------
> ##D # This model, from McArdle and Epstein (1987, p.118), illustrates the use of a 
> ##D # raw moment matrix to fit a model with an intercept. (The example was suggested
> ##D # by Mike Stoolmiller.)
> ##D 
> ##D M.McArdle <- scan()
> ##D 365.661     0           0           0           0
> ##D 503.175     719.905     0           0           0
> ##D 675.656     958.479    1303.392     0           0
> ##D 890.680    1265.846    1712.475    2278.257     0
> ##D  18.034      25.819      35.255      46.593     1.000
> ##D  
> ##D M.McArdle <- matrix(M.McArdle, 5, 5, byrow=TRUE)
> ##D rownames(M.McArdle) <- colnames(M.McArdle) <- scan(what="")
> ##D WISC1 WISC2 WISC3 WISC4 UNIT
> ##D  
> ##D mod.McArdle <- specify.model()
> ##D C -> WISC1, NA, 6.07
> ##D C -> WISC2, B2, NA
> ##D C -> WISC3, B3, NA
> ##D C -> WISC4, B4, NA
> ##D UNIT -> C, Mc, NA
> ##D C <-> C, Vc, NA,
> ##D WISC1 <-> WISC1, Vd, NA
> ##D WISC2 <-> WISC2, Vd, NA
> ##D WISC3 <-> WISC3, Vd, NA
> ##D WISC4 <-> WISC4, Vd, NA
> ##D 
> ##D sem.McArdle <- sem(mod.McArdle, M.McArdle, 204, fixed.x="UNIT", raw=TRUE)
> ##D summary(sem.McArdle)
> ##D 
> ##D ## Model fit to raw moment matrix.
> ##D ## 
> ##D ##  Model Chisquare =  83.791   Df =  8 Pr(>Chisq) = 8.4377e-15
> ##D ##  Goodness-of-fit index =  0.84537
> ##D ##  Adjusted goodness-of-fit index =  0.71007
> ##D ##  RMSEA index =  0.2155   90 
> ##D ##  BIC =  28.371 
> ##D ## 
> ##D ##  Normalized Residuals
> ##D ##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
> ##D ## -0.15300 -0.01840  0.00132 -0.00576  0.02400  0.07760 
> ##D ## 
> ##D ##  Parameter Estimates
> ##D ##    Estimate Std Error z value Pr(>|z|)                 
> ##D ## B2  8.61354 0.135438  63.5976 0        WISC2 <--- C    
> ##D ## B3 11.64054 0.168854  68.9387 0        WISC3 <--- C    
> ##D ## B4 15.40323 0.213071  72.2916 0        WISC4 <--- C    
> ##D ## Mc  3.01763 0.060690  49.7219 0        C <--- UNIT     
> ##D ## Vc  0.44343 0.047704   9.2955 0        C <--> C        
> ##D ## Vd 11.78832 0.674059  17.4885 0        WISC1 <--> WISC1
> ##D ##
> ##D ##  Iterations =  37 
> ##D     
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "specify.model"
> 
> ### * specify.model
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: specify.model
> ### Title: Specify a Structural Equation Model
> ### Aliases: specify.model print.mod
> ### Keywords: models
> 
> ### ** Examples
> 
> model.dhp <- specify.model()
1:     RParAsp  -> RGenAsp, gam11,  NA
2:     RIQ      -> RGenAsp, gam12,  NA
3:     RSES     -> RGenAsp, gam13,  NA
4:     FSES     -> RGenAsp, gam14,  NA
5:     RSES     -> FGenAsp, gam23,  NA
6:     FSES     -> FGenAsp, gam24,  NA
7:     FIQ      -> FGenAsp, gam25,  NA
8:     FParAsp  -> FGenAsp, gam26,  NA
9:     FGenAsp  -> RGenAsp, beta12, NA
10:     RGenAsp  -> FGenAsp, beta21, NA
11:     RGenAsp  -> ROccAsp,  NA,     1
12:     RGenAsp  -> REdAsp,  lam21,  NA
13:     FGenAsp  -> FOccAsp,  NA,     1
14:     FGenAsp  -> FEdAsp,  lam42,  NA
15:     RGenAsp <-> RGenAsp, ps11,   NA
16:     FGenAsp <-> FGenAsp, ps22,   NA
17:     RGenAsp <-> FGenAsp, ps12,   NA
18:     ROccAsp <-> ROccAsp, theta1, NA
19:     REdAsp  <-> REdAsp,  theta2, NA
20:     FOccAsp <-> FOccAsp, theta3, NA
21:     FEdAsp  <-> FEdAsp,  theta4, NA
22: 
Read 21 records
> model.dhp
   Path                Parameter StartValue
1  RParAsp  -> RGenAsp gam11     NA        
2  RIQ      -> RGenAsp gam12     NA        
3  RSES     -> RGenAsp gam13     NA        
4  FSES     -> RGenAsp gam14     NA        
5  RSES     -> FGenAsp gam23     NA        
6  FSES     -> FGenAsp gam24     NA        
7  FIQ      -> FGenAsp gam25     NA        
8  FParAsp  -> FGenAsp gam26     NA        
9  FGenAsp  -> RGenAsp beta12    NA        
10 RGenAsp  -> FGenAsp beta21    NA        
11 RGenAsp  -> ROccAsp <NA>       1        
12 RGenAsp  -> REdAsp  lam21     NA        
13 FGenAsp  -> FOccAsp <NA>       1        
14 FGenAsp  -> FEdAsp  lam42     NA        
15 RGenAsp <-> RGenAsp ps11      NA        
16 FGenAsp <-> FGenAsp ps22      NA        
17 RGenAsp <-> FGenAsp ps12      NA        
18 ROccAsp <-> ROccAsp theta1    NA        
19 REdAsp  <-> REdAsp  theta2    NA        
20 FOccAsp <-> FOccAsp theta3    NA        
21 FEdAsp  <-> FEdAsp  theta4    NA        
> 
> 
> 
> cleanEx(); ..nameEx <- "standardized.coefficients"
> 
> ### * standardized.coefficients
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: standardized.coefficients
> ### Title: Standardized Coefficients for Structural Equation Models
> ### Aliases: standardized.coefficients std.coef
> ### Keywords: models
> 
> ### ** Examples
> 
> 
> # ------------- assumes that Duncan, Haller and Portes peer-influences model
> # -------------     has been fit and is in sem.dhp.1     
> ## Not run: 
> ##D standardized.coefficients(sem.dhp.1) 
> ##D 
> ##D ##           Std. Estimate                     
> ##D ## 1  gam11  0.210278      RGenAsp <--- RParAsp
> ##D ## 2  gam12  0.325612      RGenAsp <--- RIQ    
> ##D ## 3  gam13  0.284855      RGenAsp <--- RSES   
> ##D ## 4  gam14  0.093702      RGenAsp <--- FSES   
> ##D ## 5  gam23  0.074576      FGenAsp <--- RSES   
> ##D ## 6  gam24  0.275763      FGenAsp <--- FSES   
> ##D ## 7  gam25  0.420558      FGenAsp <--- FIQ    
> ##D ## 8  gam26  0.192224      FGenAsp <--- FParAsp
> ##D ## 9  beta12 0.199418      RGenAsp <--- FGenAsp
> ##D ## 10 beta21 0.217521      FGenAsp <--- RGenAsp
> ##D ## 11        0.766717      ROccAsp <--- RGenAsp
> ##D ## 12 lam21  0.814771      REdAsp <--- RGenAsp 
> ##D ## 13        0.829943      FOccAsp <--- FGenAsp
> ##D ## 14 lam42  0.771619      FEdAsp <--- FGenAsp 
> ##D     
> ## End(Not run)
> 
> 
> 
> cleanEx(); ..nameEx <- "tsls"
> 
> ### * tsls
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: tsls
> ### Title: Two-Stage Least Squares
> ### Aliases: tsls tsls.formula tsls.default fitted.tsls residuals.tsls
> ###   coefficients.tsls vcov.tsls anova.tsls print.tsls summary.tsls
> ### Keywords: models
> 
> ### ** Examples
> 
> data(Kmenta)
> summary(tsls(Q ~ P + D, ~ D + F + A, data=Kmenta))     # demand equation

 2SLS Estimates

Model Formula: Q ~ P + D

Instruments: ~D + F + A

Residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-3.43e+00 -1.24e+00 -1.89e-01  5.74e-12  1.58e+00  2.49e+00 

            Estimate Std. Error t value  Pr(>|t|)
(Intercept)  94.6333    7.92084  11.947 1.076e-09
P            -0.2436    0.09648  -2.524 2.183e-02
D             0.3140    0.04694   6.689 3.811e-06

Residual standard error: 1.9663 on 17 degrees of freedom

> 
> ##  2SLS Estimates
> ##  
> ##  Model Formula: Q ~ P + D
> ##  
> ##  Instruments: ~D + F + A
> ##  
> ##  Residuals:
> ##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> ##  -3.43e+00 -1.24e+00 -1.89e-01 -2.49e-13  1.58e+00  2.49e+00 
> ##  
> ##              Estimate Std. Error t value  Pr(>|t|)
> ##  (Intercept)  94.6333    7.92084  11.947 1.076e-09
> ##  P            -0.2436    0.09648  -2.524 2.183e-02
> ##  D             0.3140    0.04694   6.689 3.811e-06
> ##  
> ##  Residual standard error: 1.9663 on 17 degrees of freedom
> 
> summary(tsls(Q ~ P + F + A, ~ D + F + A, data=Kmenta)) # supply equation

 2SLS Estimates

Model Formula: Q ~ P + F + A

Instruments: ~D + F + A

Residuals:
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-4.87e+00 -1.26e+00  6.42e-01 -2.46e-12  1.47e+00  3.49e+00 

            Estimate Std. Error t value  Pr(>|t|)
(Intercept)  49.5324   12.01053   4.124 7.954e-04
P             0.2401    0.09993   2.402 2.878e-02
F             0.2556    0.04725   5.410 5.785e-05
A             0.2529    0.09966   2.538 2.193e-02

Residual standard error: 2.4576 on 16 degrees of freedom

> 
> ##  2SLS Estimates
> ##  
> ##  Model Formula: Q ~ P + F + A
> ##  
> ##  Instruments: ~D + F + A
> ##  
> ##  Residuals:
> ##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
> ##  -4.87e+00 -1.26e+00  6.42e-01 -5.64e-12  1.47e+00  3.49e+00 
> ##  
> ##              Estimate Std. Error t value  Pr(>|t|)
> ##  (Intercept)  49.5324   12.01053   4.124 7.954e-04
> ##  P             0.2401    0.09993   2.402 2.878e-02
> ##  F             0.2556    0.04725   5.410 5.785e-05
> ##  A             0.2529    0.09966   2.538 2.193e-02
> ##  
> ##  Residual standard error: 2.4576 on 16 degrees of freedom
> 
> anova(tsls(Q ~ P + F + A, ~ D + F + A, data=Kmenta),
+     tsls(Q ~ 1, ~ D + F + A, data=Kmenta))
Analysis of Variance

Model 1:  Q ~ P + F + A   Instruments: ~D + F + A
Model 2:  Q ~ 1   Instruments: ~D + F + A

        Res.Df     RSS Df Sum of Sq      F  Pr(>F)  
Model 1     16  96.633                              
Model 2     19 268.114  3   171.481 4.0507 0.02553 *
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> ##  Analysis of Variance
> ##  
> ##  Model 1:  Q ~ P + F + A   Instruments: ~D + F + A
> ##  Model 2:  Q ~ 1   Instruments: ~D + F + A
> ##  
> ##          Res.Df     RSS Df Sum of Sq      F  Pr(>F)
> ##  Model 1     16  96.633                            
> ##  Model 2     19 268.114  3   171.481 4.0507 0.02553
> 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  6.95 0.04 7.08 0 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')