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lavaan (0.4-11) converged normally after 15 iterations!
<L3&
.+C3*&
Number of observations
90!
Estimator
Minimum Function Chi-square
Degrees of freedom
P-value
#regression!
aLM<-lm(cover ~ age, data=keeley)!
Parameter estimates:!
#sem!
library(lavaan)!
aSEM<-sem('cover ~ age', data=keeley)!
Regressions:!
cover ~!
age
T+QF<*3&)+&k3L*3771+(&
Regressions:!
cover ~!
age
Variances:!
cover
Estimate
Std.err
Z-value
P(>|z|)!
-0.009
0.002
-3.549
0.000!
0.013!
9+J*:7.!,+!f./02F:4!CE!
/R7,#@=@hB$"@=(AX!
0.087
> summary(aLM)!
Coefficients:!
Estimate Std. Error t
(Intercept) 0.917395
0.071726
age
-0.008846
0.002520
---!
Signif. codes: 0 ‘***’ 0.001 ‘**’
value Pr(>|t|)
!
12.79 < 2e-16 ***!
-3.51 0.00071 ***!
0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 !
Residual standard error: 0.2988 on 88 degrees of freedom!
iF,!j-:,!:6+F,!,-.!0;,.7<.*,k!
ML!
0.000!
0!
1.000!
Information
Standard Errors
Variances:!
cover
!"#$%&'(&()*+,)*$#&
("-&#(!!,./,!-:/!;+!2T!
Expected!
Standard!
Estimate
Std.err
Z-value
P(>|z|)!
-0.009
0.002
-3.549
0.000!
0.087
0.013!
'()3*.3F)7&:7/Q<)3,&I1)5&63<(&
9)*-.)-*3&
> aMeanSEM<-sem('cover ~ age',
data=keeley, meanstructure=T)!
> summary(aMeanSEM)!
...!
Estimate Std.err Z-value
Regressions:!
cover ~!
age
-0.009
Intercepts:!
cover
Variances:!
cover
P(>|z|)!
0.002
-3.549
0.000!
0.917
0.071
12.935
0.000!
0.087
0.013!
s&
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9)<(,<*,1b3,&T+3w.13()7&
@*1(L1(L&@<.2&\1*3&
!! !lhs op
rhs est.std
se
z pvalue!
1 cover ~
age -0.350 0.099 -3.549
0!
2 cover ~~ cover
0.877 0.131 6.708
0!
3
age ~~
age
1.000
NA
NA
NA!
d>ss&
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d>q$&
!!
!
!
Regressions:!
firesev ~!
age
cover ~!
firesev
age
Variances:!
firesev
cover
!
!Estimate
J*373C&
Z-value
.+C3*&
partialMedModel<-' firesev ~ age!
cover ~ firesev + age'!
partialMedSEM<-sem(partialMedModel, !
!! ! ! ! ! ! data=keeley)!
73QH4+)&
Sd>!$&
d>|x&
P(>|z|)
Std.lv
Std.all!
0.060
0.012
4.832
0.000
0.060
0.454!
0.020
0.003
-3.353
-1.833
0.001
0.067
-0.067
-0.005
-0.350!
-0.191!
2.144
0.078
0.320
0.012
2.144
0.078
0.794!
0.780!
0.206!
0.220!
J*373C&
d>|s&
-0.067
-0.005
R-Square:!
firesev
cover
Sd>%x&
Std.err
.+C3*&
.+C3*&
e4/+d!summary(aSEM, standardized=T, rsq=T)!
<L3&
<L3&
#plot!
library(semPlot)!
semPaths(partialMedSEM, "std")!
x&
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<7&I3&<*3&
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zeroMedModel<-' firesev ~ 0*age!
cover ~ 0*firesev + age'!
zeroMedFit<-sem(zeroMedModel, !
!! ! ! ! ! ! data=keeley)!
D5<)&<O+-)&T+**34<)3,&:**+*G&
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7)<(,<*,1b3,9+4-/+(_b3*+63,\1)`&
d&
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d>ss&
d&
!! !lhs op
rhs est.std
se
z pvalue!
1 firesev ~
age
0.000
NA
NA
NA!
2
cover ~ firesev
0.000
NA
NA
NA!
3
cover ~
age -0.350 0.099 -3.549
0!
4 firesev ~~ firesev
1.000 0.149 6.708
0!
5
cover ~~
cover
0.877 0.131 6.708
0!
6
age ~~
age
1.000
NA
NA
NA!
D5<)&<O+-)&T+**34<)3,&:**+*G&
Sd>!$&
%%&
<L3&
Sd>!$&
<L3&
.+C3*&
0.87
<L3&
J*373C&
%#&
#what about correlations!
corModel <-'firesev ~ age!
cover ~ age!
cover ~~ firesev'!
corFit <- sem(corModel, data=keeley)!
Sd>!!&
d>q$&
J*373C&
0.79
> standardizedSolution(corFit)!
lhs op
rhs est.std
se
z pvalue!
1 firesev ~
age
0.454 0.094 4.832
0!
2
cover ~
age -0.350 0.099 -3.549
0!
3 firesev ~~
cover -0.333 0.094 -3.556
0!
4 firesev ~~ firesev
0.794 0.118 6.708
0!
5
cover ~~
cover
0.877 0.131 6.708
0!
6
age ~~
age
1.000
NA
NA
NA!
%d&
!"#$"%!&
9+4-/+(&%i&[53&6+,34&
6+*(1(L&:N3*.173&
<O1+/.&
%>  \144&1(&9)<(,<*,1b3,&T+3w.13()7&<(,&k#&8+*&
)517&Q+,34&
#>  k3J)&17&<77-Q1(L&)5<)&)53*3&17&<&%i%&
*34</+(751F&O3)I33(&53)3*+&<(,&*1.5(377&
<O1+/.&
,17)<(.3&
*1.5&
,17)<(.3&
*1.5(377&
53)3*+&
#The Richness Partial Mediation Model!
distModel <- 'rich ~ distance + abiotic + hetero!
hetero ~ distance!
abiotic ~ distance'!
distFit <- sem(distModel, data=keeley)!
53)3*+&
9+4-/+(&%i&[53&6+,34&
d>qt&
,17)<(.3&
d>!$&
lhs
1
rich
2
rich
3
rich
4
hetero
5 abiotic
6
rich
7
hetero
8 abiotic
9 distance
op
~
~
~
~
~
~~
~~
~~
~~
<O1+/.&
k#Zd>#%&
d>!s&
53)3*+&
k#Zd>%#&
T+QF<*3&I1)5&H13.3I173&\1)&
d>#|&
*1.5(377&
k#Zd>qt&
d>#t&
rhs est.std
se
z pvalue!
distance
0.377 0.092 4.117 0.000!
abiotic
0.268 0.087 3.079 0.002!
hetero
0.256 0.082 3.104 0.002!
distance
0.346 0.099 3.498 0.000!
distance
0.460 0.094 4.911 0.000!
rich
0.539 0.080 6.708 0.000!
hetero
0.880 0.131 6.708 0.000!
abiotic
0.789 0.118 6.708 0.000!
distance
1.000
NA
NA
NA!
d>qt&
,17)<(.3&
d>!$&
<O1+/.&
k#Zd>#%&
d>!s&
53)3*+&
k#Zd>%#&
V0M.40-++2!
d>#|&
*1.5(377&
k#Zd>qt&
d>#t&
d>qt&
,17)<(.3&
d>!$&
<O1+/.&
k#Zd>#%&
d>!|&
53)3*+&
k#Zd>%#&
d>#t&
*1.5&
k#Zd>q|&
d>#$&
I0.<.j0/.!
%%&
!"#$"%!&
9+4-/+(&#i&[53&6+,34&
d>qt&
,17)<(.3&
d>!q&
<O1+/.&
k#Zd>#%&
:7/Q</(L&h1*3.)&<(,&'(,1*3.)&:V3.)7&
I1)5&R<Q3,&T+3w.13()7&
d>!d&
*1.5(377&
k#Zd>q%&
d>qq&
53)3*+&
k#Zd>%#&
>d%&_%`&
oneDistModel <- 'rich ~ distance + abiotic + 1*hetero!
hetero ~ distance!
abiotic ~ distance'!
oneFit<-sem(oneDistModel, data=keeley)!
summary(oneFit, stdandardized=T, rsquare=T)!
7-QQ<*A_)+)h17)\1)P&7)<(,<*,1b3,Z[P&
*7]-<*3Z[`&
!
...!
!
!
!
!Estimate
Std.err
Z-value
P(>|z|)
Std.lv
Std.all!
Defined parameters:!
direct
0.640
indirect
13.357
total
13.997
0.156
5.090
5.051
4.117
2.624
2.771
0.000
0.009
0.006
0.640
13.357
13.997
0.377!
0.210!
0.588!
totDistModel <- '!
! !rich ~ a*distance + b*abiotic + c*hetero
! !hetero ~ b1*distance
!
! !abiotic ~ c1*distance !
direct:= a
! !indirect:= b1*b + c1*c
! !total:= b1*b + c1*c + a
'!
!
!
!
!
7)<(,<*,1b3,9+4-/+(_)+)h17)\1)`&
! ! lhs op
rhs est.std
se
z
1
rich ~
distance
0.377 0.092 4.117
2
rich ~
abiotic
0.268 0.087 3.079
3
rich ~
hetero
0.256 0.082 3.104
4
hetero ~
distance
0.346 0.099 3.498
5
abiotic ~
distance
0.460 0.094 4.911
6
rich ~~
rich
0.539 0.080 6.708
7
hetero ~~
hetero
0.880 0.131 6.708
8
abiotic ~~
abiotic
0.789 0.118 6.708
9 distance ~~
distance
1.000
NA
NA
10
direct :=
a
0.377
NA
NA
11 indirect :=
b1*b+c1*c
0.210
NA
NA
12
total := b1*b+c1*c+a
0.588
NA
NA
pvalue!
0.000!
0.002!
0.002!
0.000!
0.000!
0.000!
0.000!
0.000!
NA!
NA!
NA!
NA!
%#&