Structured latent growth curve with definition variables

#variable names
manifest_vars <- names(data_wide)[str_detect(string = names(data_wide), pattern = 'obs_score')]
time_vars <- names(data_wide)[str_detect(string = names(data_wide), pattern = 'actual')]
latent_vars <- c('theta', 'alpha', 'beta', 'gamma')
measurement_days <- as.numeric(str_extract(string = names(data_wide[ 2:ncol(data_wide)]), pattern = '[^_]*$'))[1:length(time_vars)]

model <- mxModel(model = 'Definition model',
type = 'RAM', independent = T,
mxData(observed = data_wide, type = 'raw'),
manifestVars = manifest_vars,
latentVars = latent_vars,

#Residual variances; by using one label, they are assumed to all be equal (homogeneity of variance)
mxPath(from = manifest_vars,
arrows=2, free=TRUE, labels='epsilon', values = 0.04, lbound = 0),

#Latent variable covariances and variances
mxPath(from = latent_vars,
connect='unique.pairs', arrows=2,
#aa(diff_rand), ab(cov_diff_beta), ac(cov_diff_gamma), bb(beta_rand), bc(var_beta_gamma), cc(gamma_rand)
free = c(TRUE,FALSE, FALSE, FALSE,
TRUE, FALSE, FALSE,
TRUE, FALSE,
TRUE),
values=c(0.04, NA, NA, NA,
0.07, NA, NA,
15, NA,
5.6),
labels=c('theta_rand', 'NA(cov_theta_alpha)', 'NA(cov_theta_beta)', 'NA(cov_theta_gamma)',
'alpha_rand','NA(cov_alpha_beta)', 'NA(cov_alpha_gamma)',
'beta_rand', 'NA(cov_beta_gamma)',
'gamma_rand'),
lbound = c(1e-3, NA, NA, NA,
1e-3, NA, NA,
1, NA,
1),
ubound = c(2, NA, NA, NA,
2, NA, NA,
90^2, NA, 45^2)),

#Latent variable means (linear parameters). Note that the nonlinear parameters of beta and gamma do not have estimated means
mxPath(from = 'one', to = c('theta', 'alpha'), free = c(TRUE, TRUE), arrows = 1,
labels = c('theta_fixed', 'alpha_fixed'), lbound = 0, ubound = 7,
values = c(2.9, 3.3)),

#Functional constraints
mxMatrix(type = 'Full', nrow = length(manifest_vars), ncol = 1, free = TRUE,
labels = 'theta_fixed', name = 't', lbound = 0, ubound = 7, values = 2.9),
mxMatrix(type = 'Full', nrow = length(manifest_vars), ncol = 1, free = TRUE,
labels = 'alpha_fixed', name = 'a', lbound = 0, ubound = 7, values = 3.3),
mxMatrix(type = 'Full', nrow = length(manifest_vars), ncol = 1, free = TRUE,
labels = 'beta_fixed', name = 'b', lbound = 1, ubound = 360, values = 171),
mxMatrix(type = 'Full', nrow = length(manifest_vars), ncol = 1, free = TRUE,
labels = 'gamma_fixed', name = 'g', lbound = 1, ubound = 360, values = 15),

##Specifies time matrix that assumes time-structured data (model runs with this time matrix)
#mxMatrix(type = 'Full', nrow = length(time_vars), ncol = 1, free = FALSE,
# values = measurement_days[1:7],
# name = 'time'),

#Specifies time matrix with definition variables that can account for varying measurements points (i.e., time-unstructured data)
##Error occurs with this time matrix
mxMatrix(type = 'Full', nrow = length(manifest_vars), ncol = 1, free = FALSE,
labels = c("data.actual_measurement_day_0", "data.actual_measurement_day_60", "data.actual_measurement_day_120",
"data.actual_measurement_day_180", "data.actual_measurement_day_240", "data.actual_measurement_day_300",
"data.actual_measurement_day_360"), name = 'time'),

#Algebra specifying first partial derivatives;
mxAlgebra(expression = 1 - 1/(1 + exp((b - time)/g)), name="Tl"),
mxAlgebra(expression = 1/(1 + exp((b - time)/g)), name = 'Al'),
mxAlgebra(expression = -((a - t) * (exp((b - time)/g) * (1/g))/(1 + exp((b - time)/g))^2), name = 'Bl'),
mxAlgebra(expression = (a - t) * (exp((b - time)/g) * ((b - time)/g^2))/(1 + exp((b -time)/g))^2, name = 'Gl'),

#Factor loadings; all fixed and, importantly, constrained to change according to their partial derivatives (i.e., nonlinear functions)
mxPath(from = 'theta', to = manifest_vars, arrows=1, free=FALSE,
labels = c("Tl[1,1]", "Tl[2,1]", "Tl[3,1]", "Tl[4,1]", "Tl[5,1]", "Tl[6,1]", "Tl[7,1]")),
mxPath(from = 'alpha', to = manifest_vars, arrows=1, free=FALSE,
labels = c("Al[1,1]", "Al[2,1]", "Al[3,1]", "Al[4,1]", "Al[5,1]", "Al[6,1]", "Al[7,1]")),
mxPath(from='beta', to = manifest_vars, arrows=1, free=FALSE,
labels = c("Bl[1,1]", "Bl[2,1]", "Bl[3,1]", "Bl[4,1]", "Bl[5,1]", "Bl[6,1]", "Bl[7,1]")),
mxPath(from='gamma', to = manifest_vars, arrows=1, free=FALSE,
labels = c("Gl[1,1]", "Gl[2,1]", "Gl[3,1]", "Gl[4,1]", "Gl[5,1]", "Gl[6,1]", "Gl[7,1]")),

mxFitFunctionML(vector = FALSE)
)

model_results <- mxRun(model) #only get error when fitting time matrix specified with definition variables