How to get estimates of latent random slopes and random intercept

Posted on Fri, 05/03/2024 - 21:17

Victor Feagins Joined: 05/02/2024

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Hello I fit a random slope and random intercept hlm and I am wondering how to get the latent values of the random slope and intercept. From what I can tell the issue is that the latent variables exist in second level so the function mxFactorScores does not know what to do. In this example U_00 is my random intercept and U_01 is my random slope.

Here is code to simulate HLM data
library(dplyr) library(tidyr) library(OpenMx)


# Simulate Data -------------

J <- 100 #number of clusters

n_j <- 30#number of observations 
gamma_00 <- 5

gamma_10 <- 3

mu_x <- 4
sim.dat <- data.frame(J_ID = 1:J) |>

  mutate(U_0j = rnorm(J, mean = 0 , sd = 1),

         U_1j = rnorm(J, mean = 0, sd = 1),

         gamma_00 = gamma_00,

         gamma_10 = gamma_10,

         n_j = n_j) |>

  rowwise() |>

  mutate(X = list(rnorm(n_j, mu_x, sd = 1)),

         R = list(rnorm(n_j, 0, sd = 1))) |>

  unnest(cols = c(X, R)) |>

  mutate(Y = gamma_00 + U_0j + (gamma_10 + U_1j) * X + R)

sim.dat.obs <- sim.dat|> select(J_ID, X, Y) |> mutate(J_ID = as.factor(J_ID))

Here is code for openmx
## J level (Teacher) -------- J_obs <- sim.dat.obs |> select(J_ID) |> distinct()


J_cluster_name <- "J_ID"
J_latent <- c("U_0", "U_1")
J_data <- mxData(J_obs, type = "raw",

                 primaryKey = J_cluster_name)
J_var <- mxPath(from = J_latent,

                arrows = 2, values = 1,

                connect = "single")

J_cov <- mxPath(from = J_latent,

                arrows = 2, values = 0,

                connect = "unique.bivariate",

                free = FALSE)
J_model <- mxModel("Level_J", type = "RAM",

                   latentVars = J_latent,

                   J_data,

                   J_var,

                   J_cov)
## I level (Student) --------

I_obs <- mxData(sim.dat.obs, type = "raw")
I_manifest <- c("X", "Y")
I_means <- mxPath(from = "one",

                  to = c("X"),

                  labels = c("mu_x"),

                  value = 1)

I_var <- mxPath(from = c("X", "Y"),

                labels = c("sd_x", "R_ysd"),

                arrow = 2,

                value = 1)
I_fixed <- mxPath(from = c("one","X"),

                    to = "Y",

                    value = 1,

                    labels = c("gamma_00", "gamma_10"))
I_randomslope <- mxPath(from = c("Level_J.U_1"),

                          to = c("Y"),

                          labels = c("data.X"),

                          free = FALSE,

                          joinKey = J_cluster_name)
I_randomint <- mxPath(from = c("Level_J.U_0"),

                        to = c("Y"),

                        value = 1,

                        free = FALSE,

                        joinKey = J_cluster_name)
I_model<- mxModel("Level_I", type = "RAM",

                  manifestVars = I_manifest,

                  J_model,

                  I_obs,

                  I_means,

                  I_var,

                  I_fixed,

                  I_randomslope,

                  I_randomint)

I.fit <- mxRun(I_model)

#> Running Level_I with 7 parameters
summary(I.fit)

#> Summary of Level_I

#>

#> free parameters:

#>             name    matrix row col  Estimate  Std.Error A

#> 1       gamma_10         A   Y   X 3.0702452 0.09300885

#> 2           sd_x         S   X   X 0.9924763 0.02562636

#> 3          R_ysd         S   Y   Y 1.0691329 0.02857744

#> 4           mu_x         M   1   X 4.0054015 0.01818861

#> 5       gamma_00         M   1   Y 5.0011756 0.13307218

#> 6 Level_J.S[1,1] Level_J.S U_0 U_0 1.1217698 0.24712431 !

#> 7 Level_J.S[2,2] Level_J.S U_1 U_1 0.8267078 0.12055658

#>

#> Model Statistics:

#>                |  Parameters  |  Degrees of Freedom  |  Fit (-2lnL units)

#>        Model:              7                   5993              17907.01

#>    Saturated:             NA                     NA                    NA

#> Independence:             NA                     NA                    NA

#> Number of observations/statistics: 3100/6000

#>

#> Information Criteria:

#>       |  df Penalty  |  Parameters Penalty  |  Sample-Size Adjusted

#> AIC:       5921.013               17921.01                 17921.05

#> BIC:     -30271.658               17963.29                 17941.04

#> CFI: NA

#> TLI: 1   (also known as NNFI)

#> RMSEA:  0  [95% CI (NA, NA)]

#> Prob(RMSEA <= 0.05): NA

#> To get additional fit indices, see help(mxRefModels)

#> timestamp: 2024-05-03 20:11:30

#> Wall clock time: 9.318122 secs

#> optimizer:  SLSQP

#> OpenMx version number: 2.21.8

#> Need help?  See help(mxSummary)
mxFactorScores(I.fit, "WeightedML")

#> Running Container with 0 parameters

#> Error in `[.data.frame`(got, , paste0(names(coef(fit)), "SE"), drop = FALSE): undefined columns selected

mxFactorScores(I.fit@submodels$Level_J, "WeightedML") #> Error in mxEvalByName(model$expectation$M, model, compute = TRUE): 'name' argument must be a character argument

One work around I tried was to specify dummy latent variables which are the Level_J.U1 times one at the level 1 but the results were not coherent. Observations within a cluster had different values of U_1.

Replied on Fri, 05/03/2024 - 22:05

Victor Feagins Joined: 05/02/2024

I also asked on Stackoverflow

I also asked on Stackoverflow https://stackoverflow.com/questions/78427513/how-to-get-estimates-of-random-slope-and-intercept-in-openmx

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Replied on Tue, 05/21/2024 - 15:44

AdminHunter Joined: 03/01/2013

Not Implemented

Hi Victor,

Unfortunately, no such feature is currently implemented. In your specific case, it wouldn't be terribly hard for OpenMx to figure out the factor scores, but I don't think the general case (arbitrarily many levels with multiple groups and different factor structures everywhere) is solved. I don't see this feature being implemented anytime soon.

I've created an Issue on GitHub to give a better error message though: [https://github.com/OpenMx/OpenMx/issues/391](https://github.com/OpenMx/OpenMx/issues/391)