Support for extended “xtarget” rotation (loadings + factor correlations) in efa() #421
Description
I would like to request that lavaan’s exploratory factor analysis blocks support extended target rotation, allowing the simultaneous specification of target values for both factor loadings and factor correlations, as implemented in Zhang, Hattori, & Trichtinger (2019).
It would be extremely helpful if lavaan could expose that same algorithm (or a compatible interface) so that users can:
- specify a Target matrix for loadings and a PhiTarget matrix for correlations
- choose between orthogonal vs. oblique rotation of that combined criterion
Below is a minimal reprex showing the current behavior (which is as expected) and an alternative way I am using now to do it from lavaan with the help of Marco Jimenez's bifactor package:
#> #remotes::install_github("marcosjnez/bifactor")
library(lavaan)
#> This is lavaan 0.6-19
#> lavaan is FREE software! Please report any bugs.
# ─── 1. A 30×30 covariance matrix (simulate example) ───────────────────
cov_matrix <- matrix(
c(
1.081, 0.536, 0.685, 0.721, 0.679, 0.593, 0.53, 0.593, 0.522, 0.508, 0.486,
0.505, 0.611, 0.549, 0.551, 0.237, 0.178, 0.196, 0.148, 0.181, 0.196, 0.203,
0.181, 0.191, 0.235, 0.18, 0.205, -0.05, 0.121, 0.137, 0.536, 0.937, 0.493,
0.531, 0.446, 0.477, 0.463, 0.507, 0.382, 0.377, 0.419, 0.445, 0.508, 0.467,
0.389, 0.105, 0.032, 0.095, 0.039, 0.067, 0.107, 0.093, 0.088, 0.139, 0.125,
0.038, 0.141, 0.043, 0.04, 0.124, 0.685, 0.493, 1.017, 0.568, 0.569, 0.459,
0.402, 0.45, 0.45, 0.36, 0.387, 0.445, 0.533, 0.49, 0.424, 0.176, 0.149,
0.136, 0.057, 0.101, 0.224, 0.25, 0.158, 0.232, 0.291, 0.171, 0.208, -0.014,
0.143, 0.167, 0.721, 0.531, 0.568, 1.047, 0.593, 0.527, 0.524, 0.532, 0.409,
0.419, 0.384, 0.479, 0.561, 0.488, 0.48, 0.195, 0.184, 0.173, 0.179, 0.187,
0.189, 0.165, 0.249, 0.135, 0.216, 0.185, 0.178, 0.019, 0.118, 0.143, 0.679,
0.446, 0.569, 0.593, 0.987, 0.485, 0.399, 0.455, 0.378, 0.361, 0.398, 0.411,
0.514, 0.426, 0.377, 0.255, 0.135, 0.099, 0.178, 0.176, 0.273, 0.22, 0.143,
0.167, 0.207, 0.195, 0.16, -0.014, 0.161, 0.203, 0.593, 0.477, 0.459, 0.527,
0.485, 1.063, 0.551, 0.629, 0.58, 0.576, 0.385, 0.403, 0.492, 0.357, 0.432,
0.147, 0.146, 0.137, 0.145, 0.161, 0.145, 0.171, 0.183, 0.189, 0.232, 0.183,
0.203, -0.023, 0.155, 0.148, 0.53, 0.463, 0.402, 0.524, 0.399, 0.551, 1.079,
0.644, 0.464, 0.499, 0.436, 0.454, 0.549, 0.437, 0.409, 0.151, 0.178, 0.143,
0.175, 0.17, 0.145, 0.155, 0.159, 0.211, 0.219, 0.211, 0.23, 0.03, 0.166,
0.103, 0.593, 0.507, 0.45, 0.532, 0.455, 0.629, 0.644, 0.958, 0.595, 0.52,
0.423, 0.411, 0.559, 0.427, 0.455, 0.194, 0.184, 0.138, 0.18, 0.127, 0.153,
0.134, 0.185, 0.219, 0.205, 0.143, 0.221, 0.001, 0.068, 0.145, 0.522, 0.382,
0.45, 0.409, 0.378, 0.58, 0.464, 0.595, 1.007, 0.482, 0.4, 0.358, 0.488,
0.437, 0.442, 0.118, 0.119, 0.049, 0.035, 0.041, 0.1, 0.134, 0.106, 0.09,
0.145, -0.009, 0.081, -0.129, -0.063, 0.067, 0.508, 0.377, 0.36, 0.419, 0.361,
0.576, 0.499, 0.52, 0.482, 0.913, 0.355, 0.353, 0.384, 0.355, 0.344, 0.13,
0.167, 0.116, 0.135, 0.102, 0.156, 0.113, 0.124, 0.166, 0.146, 0.14, 0.167,
0.051, 0.036, 0.109, 0.486, 0.419, 0.387, 0.384, 0.398, 0.385, 0.436, 0.423,
0.4, 0.355, 0.87, 0.601, 0.549, 0.541, 0.446, 0.129, 0.124, 0.056, 0.102,
0.088, 0.08, 0.142, 0.1, 0.08, 0.133, 0.068, 0.08, 0.004, 0.141, 0.132, 0.505,
0.445, 0.445, 0.479, 0.411, 0.403, 0.454, 0.411, 0.358, 0.353, 0.601, 0.964,
0.575, 0.606, 0.431, 0.124, 0.089, 0.097, 0.138, 0.057, 0.081, 0.123, 0.162,
0.101, 0.119, 0.159, 0.164, 0.036, 0.138, 0.15, 0.611, 0.508, 0.533, 0.561,
0.514, 0.492, 0.549, 0.559, 0.488, 0.384, 0.549, 0.575, 0.923, 0.596, 0.509,
0.083, 0.156, 0.062, 0.11, 0.099, 0.184, 0.122, 0.142, 0.122, 0.163, 0.135,
0.099, -0.03, 0.053, 0.113, 0.549, 0.467, 0.49, 0.488, 0.426, 0.357, 0.437,
0.427, 0.437, 0.355, 0.541, 0.606, 0.596, 0.893, 0.455, 0.111, 0.075, 0.123,
0.13, 0.049, 0.071, 0.192, 0.139, 0.085, 0.175, 0.137, 0.149, 0.047, 0.078,
0.182, 0.551, 0.389, 0.424, 0.48, 0.377, 0.432, 0.409, 0.455, 0.442, 0.344,
0.446, 0.431, 0.509, 0.455, 0.828, 0.112, 0.103, 0.093, 0.13, 0.139, 0.047,
0.076, 0.055, 0.077, 0.165, 0.079, 0.136, -0.09, 0.07, 0.084, 0.237, 0.105,
0.176, 0.195, 0.255, 0.147, 0.151, 0.194, 0.118, 0.13, 0.129, 0.124, 0.083,
0.111, 0.112, 1.022, 0.7, 0.674, 0.597, 0.623, 0.514, 0.441, 0.51, 0.366,
0.517, 0.434, 0.503, 0.393, 0.612, 0.591, 0.178, 0.032, 0.149, 0.184, 0.135,
0.146, 0.178, 0.184, 0.119, 0.167, 0.124, 0.089, 0.156, 0.075, 0.103, 0.7,
1.229, 0.803, 0.732, 0.704, 0.644, 0.55, 0.614, 0.508, 0.703, 0.531, 0.565,
0.475, 0.723, 0.727, 0.196, 0.095, 0.136, 0.173, 0.099, 0.137, 0.143, 0.138,
0.049, 0.116, 0.056, 0.097, 0.062, 0.123, 0.093, 0.674, 0.803, 1.061, 0.769,
0.609, 0.569, 0.532, 0.675, 0.466, 0.655, 0.542, 0.593, 0.451, 0.652, 0.702,
0.148, 0.039, 0.057, 0.179, 0.178, 0.145, 0.175, 0.18, 0.035, 0.135, 0.102,
0.138, 0.11, 0.13, 0.13, 0.597, 0.732, 0.769, 1.152, 0.647, 0.474, 0.454,
0.522, 0.378, 0.526, 0.504, 0.45, 0.354, 0.57, 0.624, 0.181, 0.067, 0.101,
0.187, 0.176, 0.161, 0.17, 0.127, 0.041, 0.102, 0.088, 0.057, 0.099, 0.049,
0.139, 0.623, 0.704, 0.609, 0.647, 1.083, 0.493, 0.454, 0.529, 0.371, 0.533,
0.445, 0.458, 0.291, 0.568, 0.577, 0.196, 0.107, 0.224, 0.189, 0.273, 0.145,
0.145, 0.153, 0.1, 0.156, 0.08, 0.081, 0.184, 0.071, 0.047, 0.514, 0.644,
0.569, 0.474, 0.493, 0.939, 0.57, 0.552, 0.503, 0.669, 0.478, 0.489, 0.365,
0.503, 0.584, 0.203, 0.093, 0.25, 0.165, 0.22, 0.171, 0.155, 0.134, 0.134,
0.113, 0.142, 0.123, 0.122, 0.192, 0.076, 0.441, 0.55, 0.532, 0.454, 0.454,
0.57, 1.06, 0.554, 0.556, 0.644, 0.483, 0.42, 0.322, 0.399, 0.556, 0.181,
0.088, 0.158, 0.249, 0.143, 0.183, 0.159, 0.185, 0.106, 0.124, 0.1, 0.162,
0.142, 0.139, 0.055, 0.51, 0.614, 0.675, 0.522, 0.529, 0.552, 0.554, 1.011,
0.53, 0.671, 0.544, 0.516, 0.352, 0.562, 0.636, 0.191, 0.139, 0.232, 0.135,
0.167, 0.189, 0.211, 0.219, 0.09, 0.166, 0.08, 0.101, 0.122, 0.085, 0.077,
0.366, 0.508, 0.466, 0.378, 0.371, 0.503, 0.556, 0.53, 0.997, 0.61, 0.409,
0.452, 0.273, 0.473, 0.498, 0.235, 0.125, 0.291, 0.216, 0.207, 0.232, 0.219,
0.205, 0.145, 0.146, 0.133, 0.119, 0.163, 0.175, 0.165, 0.517, 0.703, 0.655,
0.526, 0.533, 0.669, 0.644, 0.671, 0.61, 1, 0.476, 0.53, 0.338, 0.568, 0.605,
0.18, 0.038, 0.171, 0.185, 0.195, 0.183, 0.211, 0.143, -0.009, 0.14, 0.068,
0.159, 0.135, 0.137, 0.079, 0.434, 0.531, 0.542, 0.504, 0.445, 0.478, 0.483,
0.544, 0.409, 0.476, 1.029, 0.469, 0.419, 0.561, 0.613, 0.205, 0.141, 0.208,
0.178, 0.16, 0.203, 0.23, 0.221, 0.081, 0.167, 0.08, 0.164, 0.099, 0.149,
0.136, 0.503, 0.565, 0.593, 0.45, 0.458, 0.489, 0.42, 0.516, 0.452, 0.53,
0.469, 1.018, 0.393, 0.655, 0.612, -0.05, 0.043, -0.014, 0.019, -0.014,
-0.023, 0.03, 0.001, -0.129, 0.051, 0.004, 0.036, -0.03, 0.047, -0.09, 0.393,
0.475, 0.451, 0.354, 0.291, 0.365, 0.322, 0.352, 0.273, 0.338, 0.419, 0.393,
0.976, 0.497, 0.563, 0.121, 0.04, 0.143, 0.118, 0.161, 0.155, 0.166, 0.068,
-0.063, 0.036, 0.141, 0.138, 0.053, 0.078, 0.07, 0.612, 0.723, 0.652, 0.57,
0.568, 0.503, 0.399, 0.562, 0.473, 0.568, 0.561, 0.655, 0.497, 1.153, 0.701,
0.137, 0.124, 0.167, 0.143, 0.203, 0.148, 0.103, 0.145, 0.067, 0.109, 0.132,
0.15, 0.113, 0.182, 0.084, 0.591, 0.727, 0.702, 0.624, 0.577, 0.584, 0.556,
0.636, 0.498, 0.605, 0.613, 0.612, 0.563, 0.701, 1.15
),
nrow = 30L,
ncol = 30L,
dimnames = list(
c(
"Item1", "Item2", "Item3", "Item4", "Item5", "Item6", "Item7", "Item8",
"Item9", "Item10", "Item11", "Item12", "Item13", "Item14", "Item15", "Item16",
"Item17", "Item18", "Item19", "Item20", "Item21", "Item22", "Item23",
"Item24", "Item25", "Item26", "Item27", "Item28", "Item29", "Item30"
),
c(
"Item1", "Item2", "Item3", "Item4", "Item5", "Item6", "Item7", "Item8",
"Item9", "Item10", "Item11", "Item12", "Item13", "Item14", "Item15", "Item16",
"Item17", "Item18", "Item19", "Item20", "Item21", "Item22", "Item23",
"Item24", "Item25", "Item26", "Item27", "Item28", "Item29", "Item30"
)
)
)
# ─── 2. Define a bifactor “target” for the 30×8 loading matrix ──────────
Target <- psych::make.keys(
30,
list(
FG1 = 1:15,
FG2 = 16:30,
FE1 = 1:5,
FE2 = 6:10,
FE3 = 11:15,
FE4 = 16:20,
FE5 = 21:25,
FE6 = 26:30
)
)
Target
#> FG1 FG2 FE1 FE2 FE3 FE4 FE5 FE6
#> [1,] 1 0 1 0 0 0 0 0
#> [2,] 1 0 1 0 0 0 0 0
#> [3,] 1 0 1 0 0 0 0 0
#> [4,] 1 0 1 0 0 0 0 0
#> [5,] 1 0 1 0 0 0 0 0
#> [6,] 1 0 0 1 0 0 0 0
#> [7,] 1 0 0 1 0 0 0 0
#> [8,] 1 0 0 1 0 0 0 0
#> [9,] 1 0 0 1 0 0 0 0
#> [10,] 1 0 0 1 0 0 0 0
#> [11,] 1 0 0 0 1 0 0 0
#> [12,] 1 0 0 0 1 0 0 0
#> [13,] 1 0 0 0 1 0 0 0
#> [14,] 1 0 0 0 1 0 0 0
#> [15,] 1 0 0 0 1 0 0 0
#> [16,] 0 1 0 0 0 1 0 0
#> [17,] 0 1 0 0 0 1 0 0
#> [18,] 0 1 0 0 0 1 0 0
#> [19,] 0 1 0 0 0 1 0 0
#> [20,] 0 1 0 0 0 1 0 0
#> [21,] 0 1 0 0 0 0 1 0
#> [22,] 0 1 0 0 0 0 1 0
#> [23,] 0 1 0 0 0 0 1 0
#> [24,] 0 1 0 0 0 0 1 0
#> [25,] 0 1 0 0 0 0 1 0
#> [26,] 0 1 0 0 0 0 0 1
#> [27,] 0 1 0 0 0 0 0 1
#> [28,] 0 1 0 0 0 0 0 1
#> [29,] 0 1 0 0 0 0 0 1
#> [30,] 0 1 0 0 0 0 0 1
# ─── 3. Define a 8×8 target for factor correlations ────────────────────
Phi_Target <- matrix(0, 8, 8)
Phi_Target[1:2, 1:2] <- 1
diag(Phi_Target) <- 0
Phi_Target
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0 1 0 0 0 0 0 0
#> [2,] 1 0 0 0 0 0 0 0
#> [3,] 0 0 0 0 0 0 0 0
#> [4,] 0 0 0 0 0 0 0 0
#> [5,] 0 0 0 0 0 0 0 0
#> [6,] 0 0 0 0 0 0 0 0
#> [7,] 0 0 0 0 0 0 0 0
#> [8,] 0 0 0 0 0 0 0 0
# ─── 4. EFA in lavaan with “target” rotation (loadings only) ────────────
# – orthogonal
fit_efaT_orth <- efa(
sample.cov = cov_matrix,
sample.nobs = 200,
nfactor = 8,
rotation = "target",
rotation.args = list(target = psych::scrub(Target,isvalue=1),
rstarts = 10L,
orthogonal = TRUE)
)
#> Warning: lavaan->lav_model_vcov():
#> The variance-covariance matrix of the estimated parameters (vcov) does not
#> appear to be positive definite! The smallest eigenvalue (= -2.320460e-18)
#> is smaller than zero. This may be a symptom that the model is not
#> identified.
# → ALL factor covariances are forced to zero
lavInspect(fit_efaT_orth$nf8, "cor.lv")
#> f1 f2 f3 f4 f5 f6 f7 f8
#> f1 1
#> f2 0 1
#> f3 0 0 1
#> f4 0 0 0 1
#> f5 0 0 0 0 1
#> f6 0 0 0 0 0 1
#> f7 0 0 0 0 0 0 1
#> f8 0 0 0 0 0 0 0 1
# – oblique
fit_efaT_oblq <- efa(
sample.cov = cov_matrix,
sample.nobs = 200,
nfactor = 8,
rotation = "target",
rotation.args = list(target = psych::scrub(Target,isvalue=1),
rstarts = 10L,
orthogonal = FALSE)
)
#> Warning: lavaan->lav_model_vcov():
#> The variance-covariance matrix of the estimated parameters (vcov) does not
#> appear to be positive definite! The smallest eigenvalue (= -2.381606e-18)
#> is smaller than zero. This may be a symptom that the model is not
#> identified.
# → STILL no way to set some Φ(i,j)=0 and others ≠0
lavInspect(fit_efaT_oblq$nf8, "cor.lv")
#> f1 f2 f3 f4 f5 f6 f7 f8
#> f1 1.000
#> f2 0.184 1.000
#> f3 -0.063 0.099 1.000
#> f4 -0.060 0.031 0.206 1.000
#> f5 -0.242 -0.022 0.193 0.109 1.000
#> f6 0.048 -0.167 0.026 0.066 -0.069 1.000
#> f7 0.177 -0.124 0.098 0.053 -0.137 0.244 1.000
#> f8 0.001 0.037 0.040 0.037 0.018 0.147 0.045 1.000
# ─── 5. External “xtarget” rotation via Marco Jimenez's bifactor package ---
fit_efaT_rotnone <- efa(
sample.cov = cov_matrix,
sample.nobs = 200,
nfactor = 8,
rotation = "none"
)
bifactor::rotate(
fit_efaT_rotnone$loadings,
rotation = "xtarget",
Target = Target,
PhiTarget = Phi_Target,
random_starts = 10L
)
#> $lambda
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.835624329 -0.01575589 0.262831832 -0.026693388 -0.064131181
#> [2,] 0.682938994 -0.01857124 0.079581863 0.085366632 0.069752566
#> [3,] 0.695276347 0.02701210 0.237840418 -0.104464412 -0.009492177
#> [4,] 0.733948369 0.03285039 0.229061750 0.003663162 -0.036348135
#> [5,] 0.627640836 0.05020864 0.543412093 0.022106420 0.052715212
#> [6,] 0.658089914 0.02336350 0.049994608 0.378924803 -0.086555036
#> [7,] 0.622807073 0.05562661 -0.047841607 0.347255104 0.083056681
#> [8,] 0.714836072 0.02805528 -0.014900701 0.450508405 -0.007145501
#> [9,] 0.638513945 -0.10165916 -0.041266494 0.314213207 0.052084914
#> [10,] 0.585303336 0.03679680 0.009879982 0.372910602 -0.021405260
#> [11,] 0.635038404 -0.02090932 -0.001628670 0.060450476 0.515601510
#> [12,] 0.663099527 0.02833035 -0.023384492 -0.047463033 0.440054659
#> [13,] 0.751191234 -0.03815962 0.113196407 0.111360986 0.337368482
#> [14,] 0.731966004 0.02551003 -0.050888900 -0.135818831 0.390752733
#> [15,] 0.709539160 -0.08956076 -0.013304536 0.038844001 0.158609682
#> [16,] 0.041595207 0.67347320 0.116065874 0.005886479 -0.021087316
#> [17,] -0.041443995 0.75972187 -0.020249359 0.076465653 0.039619011
#> [18,] 0.019685428 0.82604400 -0.167101548 -0.126393524 -0.128501997
#> [19,] 0.004550938 0.67857600 -0.041007835 0.009282449 0.037716469
#> [20,] -0.022336119 0.62250962 0.093767809 0.049649582 0.007518089
#> [21,] -0.027906305 0.71888281 0.206205225 0.057197102 0.007475502
#> [22,] 0.024783250 0.62927064 0.048563544 -0.045779224 0.052466389
#> [23,] 0.037683631 0.73477219 -0.092748380 -0.028000192 -0.038060430
#> [24,] 0.043721649 0.58720302 -0.027015967 0.087804764 -0.074691623
#> [25,] 0.066764992 0.71956008 -0.062302721 -0.027582506 -0.028665038
#> [26,] 0.021843216 0.67399810 0.069876460 0.013246839 0.008245823
#> [27,] 0.089649646 0.66707875 -0.062681210 0.031729523 -0.090051624
#> [28,] -0.170753779 0.65504410 -0.023197885 0.013379040 0.073006476
#> [29,] -0.043735954 0.74280321 0.023930400 -0.036410184 0.049753057
#> [30,] -0.032020449 0.81129260 0.029596839 -0.007799884 0.092948912
#> [,6] [,7] [,8]
#> [1,] 0.077525550 0.0047933958 0.006212683
#> [2,] -0.121243398 -0.0649669609 -0.049314414
#> [3,] -0.104823839 0.1644374559 0.044790474
#> [4,] 0.032369396 -0.0484715275 -0.030338206
#> [5,] 0.008760684 0.0082123258 0.011153656
#> [6,] -0.016656154 0.0166319921 0.085055387
#> [7,] -0.021621941 -0.0159910195 0.061576959
#> [8,] 0.017306095 -0.0115357262 -0.044619230
#> [9,] 0.072334612 0.1151253378 -0.070425903
#> [10,] -0.014089724 -0.0448326108 -0.080352942
#> [11,] 0.044327778 0.0070253862 0.084784818
#> [12,] -0.072904030 -0.0917605953 0.012328056
#> [13,] 0.006446903 0.0493125947 -0.038118457
#> [14,] -0.087622136 -0.0347490298 -0.068170219
#> [15,] 0.168209109 0.0337583227 0.061229024
#> [16,] 0.331000912 -0.0215849424 0.058657105
#> [17,] 0.352227913 0.1297643392 0.067552096
#> [18,] 0.320861212 0.0008929858 -0.038311584
#> [19,] 0.417549682 -0.0738463668 -0.045976494
#> [20,] 0.398265854 0.0733516828 0.049734260
#> [21,] 0.061497963 0.3498103354 -0.047100788
#> [22,] -0.010744412 0.3764476856 -0.126606853
#> [23,] 0.050519389 0.2253631784 -0.009090946
#> [24,] -0.101979099 0.3745765367 0.061729740
#> [25,] 0.087428530 0.5173444960 0.039010887
#> [26,] -0.044748758 0.0005128910 0.021508323
#> [27,] -0.025672176 0.0333863110 0.169974440
#> [28,] -0.134697955 -0.1446123761 0.002460289
#> [29,] 0.053285364 -0.0425883798 0.665594093
#> [30,] 0.021059097 0.0086155293 0.012858168
#>
#> $phi
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 1.000000000 0.238360783 -0.022592342 -0.007122988 -0.026547614
#> [2,] 0.238360783 1.000000000 0.035255840 0.007226791 -0.013789461
#> [3,] -0.022592342 0.035255840 1.000000000 0.034751174 0.029990084
#> [4,] -0.007122988 0.007226791 0.034751174 1.000000000 0.017970646
#> [5,] -0.026547614 -0.013789461 0.029990084 0.017970646 1.000000000
#> [6,] 0.017001583 -0.029147213 0.005870422 0.018977533 -0.021236348
#> [7,] 0.079201816 -0.034037832 0.037215672 0.018941822 -0.035596461
#> [8,] -0.014275659 0.006501432 0.006736975 0.003063213 0.005334851
#> [,6] [,7] [,8]
#> [1,] 0.017001583 0.079201816 -0.014275659
#> [2,] -0.029147213 -0.034037832 0.006501432
#> [3,] 0.005870422 0.037215672 0.006736975
#> [4,] 0.018977533 0.018941822 0.003063213
#> [5,] -0.021236348 -0.035596461 0.005334851
#> [6,] 1.000000000 0.057264211 0.034944765
#> [7,] 0.057264211 1.000000000 0.001343973
#> [8,] 0.034944765 0.001343973 1.000000000
#>
#> $propVar
#> [,1]
#> [1,] 0.23719048
#> [2,] 0.24596254
#> [3,] 0.02033770
#> [4,] 0.02662238
#> [5,] 0.02698824
#> [6,] 0.02581150
#> [7,] 0.02731267
#> [8,] 0.01881867
#>
#> $T
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 0.947044542 0.21808295 0.27542694 -0.02648640 -0.09189072 -0.1085639959
#> [2,] 0.226650743 0.04637946 -0.38400954 0.33999225 0.41437209 0.6378136714
#> [3,] -0.002163568 0.14288525 0.14977450 -0.38004299 0.09996736 0.5567453890
#> [4,] -0.101764463 0.74114980 0.41515268 -0.06726609 -0.04207702 0.1723377513
#> [5,] -0.186170061 -0.31811923 0.73152453 0.39718290 0.46325776 0.0285104482
#> [6,] 0.014371977 0.33455110 -0.05338893 0.73364476 -0.36502975 0.0009070993
#> [7,] 0.080193534 0.40635508 -0.20935183 -0.02034083 0.67735253 -0.4535682331
#> [8,] -0.008862378 -0.04817491 0.00926401 0.19581546 0.03777562 -0.1876273970
#> [,7] [,8]
#> [1,] 0.099929194 -0.00200556
#> [2,] -0.274454935 -0.21279873
#> [3,] 0.635251060 0.17336827
#> [4,] -0.369693359 -0.28366871
#> [5,] 0.008537593 0.12375255
#> [6,] 0.317540086 0.32446399
#> [7,] 0.149516739 0.23046027
#> [8,] 0.501210239 -0.81883129
#>
#> $f
#> [1] 0.3847984
#>
#> $iterations
#> [1] 67
#>
#> $convergence
#> [1] TRUE
#>
#> $elapsed
#> elapsed
#> 30891600
#>
#> attr(,"class")
#> [1] "rotation"Created on 2025-04-19 with reprex v2.1.1
Session info
sessioninfo::session_info()
#> Warning in system2("quarto", "-V", stdout = TRUE, env = paste0("TMPDIR=", : el
#> comando ejecutado '"quarto"
#> TMPDIR=C:/Users/brian/AppData/Local/Temp/RtmpMH4ODr/file5e3435b12706 -V' tiene
#> el estatus 1
#> ─ Session info ───────────────────────────────────────────────────────────────
#> setting value
#> version R version 4.4.3 (2025-02-28 ucrt)
#> os Windows 11 x64 (build 26100)
#> system x86_64, mingw32
#> ui RTerm
#> language (EN)
#> collate Spanish_Peru.utf8
#> ctype Spanish_Peru.utf8
#> tz Europe/Paris
#> date 2025-04-19
#> pandoc 3.2 @ C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)
#> quarto NA @ C:\\PROGRA~1\\Quarto\\bin\\quarto.exe
#>
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#> package * version date (UTC) lib source
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#> cli 3.6.4 2025-02-13 [1] CRAN (R 4.4.3)
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#> evaluate 1.0.3 2025-01-10 [1] CRAN (R 4.4.2)
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#> numDeriv 2016.8-1.1 2019-06-06 [1] CRAN (R 4.4.0)
#> pbivnorm 0.6.0 2015-01-23 [1] CRAN (R 4.4.0)
#> psych 2.5.3 2025-03-21 [1] CRAN (R 4.4.3)
#> quadprog 1.5-8 2019-11-20 [1] CRAN (R 4.4.0)
#> Rcpp 1.0.14 2025-01-12 [1] CRAN (R 4.4.2)
#> reprex 2.1.1 2024-07-06 [1] CRAN (R 4.4.1)
#> rlang 1.1.6 2025-04-11 [1] CRAN (R 4.4.3)
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#> xfun 0.52 2025-04-02 [1] CRAN (R 4.4.3)
#> yaml 2.3.10 2024-07-26 [1] CRAN (R 4.4.1)
#>
#> [1] C:/Users/brian/AppData/Local/R/win-library/4.4
#> [2] C:/Program Files/R/R-4.4.3/library
#> * ── Packages attached to the search path.
#>
#> ──────────────────────────────────────────────────────────────────────────────