Notes

1. No success running this path analysis

> andow <- file.choose()
> andow1 <- read.csv(andow, sep = ";")
> View(andow1)
> require(lavaan)
Loading required package: lavaan
This is lavaan 0.5-23.1097
lavaan is BETA software! Please report any bugs.
> model<-'
+ m1~x
+ m2~m1+x
+ y~m2+m1+x
+ '
> typeof(andow1)
[1] "list"
> andow1 <- as.matrix(andow1)
> nrow(andow1)
[1] 196
> results<-sem(model,sample.cov=andow1,sample.nobs=nrow(andow1))
Error in lav_samplestats_icov(COV = cov[[g]], ridge = ridge, x.idx = x.idx[[g]], :
lavaan ERROR: sample covariance matrix is not positive-definite
In addition: Warning message:
In tmp.cov[upper.tri(tmp.cov)] <- T[upper.tri(T)] :
number of items to replace is not a multiple of replacement length


2. y but not m2 demonstrates differences by condition and antirealism

. pwcorr x m1 m2 y, sig obs

| x m1 m2 y
-------------+------------------------------------
x | 1.0000
|
| 196
|
m1 | 0.5325 1.0000
| 0.0000
| 196 196
|
m2 | -0.0840 0.0701 1.0000
| 0.2415 0.3289
| 196 196 196
|
y | 0.6204 0.4631 0.0521 1.0000
| 0.0000 0.0000 0.4687
| 196 196 196 196
|


3. first-person justification doesn't seem to be predicted by domain or antirealism

. anova m2 x##m1

Number of obs = 196 R-squared = 0.0300
Root MSE = 47.8662 Adj R-squared = 0.0148

Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 13582.8864 3 4527.62881 1.98 0.1189
|
x | 995.552199 1 995.552199 0.43 0.5106
m1 | 1432.97297 1 1432.97297 0.63 0.4300
x#m1 | 2028.77183 1 2028.77183 0.89 0.3479
|
Residual | 439905.2 192 2291.17292
-----------+----------------------------------------------------
Total | 453488.087 195 2325.57993

4. testimonial justification does

. anova y x##m1

Number of obs = 196 R-squared = 0.4118
Root MSE = 41.1874 Adj R-squared = 0.4026

Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 228062.641 3 76020.8803 44.81 0.0000
|
x | 37722.4041 1 37722.4041 22.24 0.0000
m1 | 12284.8053 1 12284.8053 7.24 0.0078
x#m1 | 1296.68928 1 1296.68928 0.76 0.3831
|
Residual | 325708.859 192 1696.40031
-----------+----------------------------------------------------
Total | 553771.5 195 2839.85385

5. when domain = 1, testimony is much less justified, especially among those for whom M1 = 0.

. mean m2 y, over(x m1)

Mean estimation Number of obs = 196

Over: x m1
_subpop_1: 1 0
_subpop_2: 1 1
_subpop_3: 2 0
_subpop_4: 2 1

--------------------------------------------------------------
Over | Mean Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
m2 |
_subpop_1 | 54.50526 5.05688 44.53206 64.47846
_subpop_2 | 52.7 20.27782 12.708 92.692
_subpop_3 | 35.26667 7.447317 20.57904 49.95429
_subpop_4 | 56.08824 6.055539 44.14548 68.03099
-------------+------------------------------------------------
y |
_subpop_1 | -45.08421 4.620168 -54.19612 -35.9723
_subpop_2 | -8.2 31.94159 -71.19533 54.79533
_subpop_3 | 12.74444 5.139951 2.607412 22.88148
_subpop_4 | 31.53922 4.945762 21.78516 41.29327
--------------------------------------------------------------

6. but that interaction term is still shy of significance, p = .17.

. gen diff = y - m2

. mean diff, over(x m1)

Mean estimation Number of obs = 196

Over: x m1
_subpop_1: 1 0
_subpop_2: 1 1
_subpop_3: 2 0
_subpop_4: 2 1

--------------------------------------------------------------
Over | Mean Std. Err. [95% Conf. Interval]
-------------+------------------------------------------------
diff |
_subpop_1 | -99.58947 6.516668 -112.4417 -86.73727
_subpop_2 | -60.9 36.44805 -132.783 10.98298
_subpop_3 | -22.52222 8.628236 -39.53886 -5.505581
_subpop_4 | -24.54902 7.031055 -38.4157 -10.68234
--------------------------------------------------------------

. anova diff x##m1

Number of obs = 196 R-squared = 0.2888
Root MSE = 59.4797 Adj R-squared = 0.2777

Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 275827.006 3 91942.3354 25.99 0.0000
|
x | 50974.3215 1 50974.3215 14.41 0.0002
m1 | 5326.40319 1 5326.40319 1.51 0.2213
x#m1 | 6569.33945 1 6569.33945 1.86 0.1746
|
Residual | 679264.295 192 3537.83487
-----------+----------------------------------------------------
Total | 955091.301 195 4897.90411


7.

8. There are, however, a number of interaction effects trending as shown in this ME model.

. xtmixed resp x##m1##c.test || id: test,

Performing EM optimization:

Performing gradient-based optimization:

Iteration 0: log likelihood = -2044.7512
Iteration 1: log likelihood = -2040.2297
Iteration 2: log likelihood = -2040.1043
Iteration 3: log likelihood = -2040.095
Iteration 4: log likelihood = -2040.0949

Computing standard errors:

Mixed-effects ML regression Number of obs = 392
Group variable: id Number of groups = 196

Obs per group: min = 2
avg = 2.0
max = 2


Wald chi2(7) = 340.41
Log likelihood = -2040.0949 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
resp | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
2.x | -96.30585 17.05728 -5.65 0.000 -129.7375 -62.87419
1.m1 | -40.49474 43.2481 -0.94 0.349 -125.2595 44.26998
|
x#m1 |
2 1 | 63.3431 47.35011 1.34 0.181 -29.46141 156.1476
|
test | -99.58947 6.039909 -16.49 0.000 -111.4275 -87.75147
|
x#c.test |
2 | 77.06725 10.6534 7.23 0.000 56.18697 97.94753
|
m1#c.test |
1 | 38.68947 27.01129 1.43 0.152 -14.25169 91.63064
|
x#m1#c.test |
2 1 | -40.71627 29.57327 -1.38 0.169 -98.67881 17.24627
|
_cons | 154.0947 9.670569 15.93 0.000 135.1408 173.0487
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
id: Independent |
sd(test) | .0000318 .0000445 2.05e-06 .0004938
sd(_cons) | 14.84158 4.729686 7.947321 27.71656
-----------------------------+------------------------------------------------
sd(Residual) | 41.6272 2.102502 37.70377 45.9589
------------------------------------------------------------------------------
LR test vs. linear regression: chi2(2) = 2.51 Prob > chi2 = 0.2852

Note: LR test is conservative and provided only for reference.

.