```
predict(
.object = NULL,
.benchmark = c("lm", "unit", "PLS-PM", "GSCA", "PCA", "MAXVAR", "NA"),
.approach_predict = c("earliest", "direct"),
.cv_folds = 10,
.handle_inadmissibles = c("stop", "ignore", "set_NA"),
.r = 1,
.test_data = NULL,
.approach_score_target = c("mean", "median", "mode"),
.sim_points = 100,
.disattenuate = TRUE,
.treat_as_continuous = TRUE,
.approach_score_benchmark = c("mean", "median", "mode", "round"),
.seed = NULL
)
```

- .object
An R object of class cSEMResults resulting from a call to

`csem()`

.- .benchmark
Character string. The procedure to obtain benchmark predictions. One of "

*lm*", "*unit*", "*PLS-PM*", "*GSCA*", "*PCA*", "*MAXVAR*", or "*NA*". Default to "*lm*".- .approach_predict
Character string. Which approach should be used to perform predictions? One of "

*earliest*" and "*direct*". If "*earliest*" predictions for indicators associated to endogenous constructs are performed using only indicators associated to exogenous constructs. If "*direct*", predictions for indicators associated to endogenous constructs are based on indicators associated to their direct antecedents. Defaults to "*earliest*".- .cv_folds
Integer. The number of cross-validation folds to use. Setting

`.cv_folds`

to`N`

(the number of observations) produces leave-one-out cross-validation samples. Defaults to`10`

.- .handle_inadmissibles
Character string. How should inadmissible results be treated? One of "

*stop*", "*ignore*", or "*set_NA*". If "*stop*",`predict()`

will stop immediately if estimation yields an inadmissible result. For "*ignore*" all results are returned even if all or some of the estimates yielded inadmissible results. For "*set_NA*" predictions based on inadmissible parameter estimates are set to`NA`

. Defaults to "*stop*"- .r
Integer. The number of repetitions to use. Defaults to

`1`

.- .test_data
A matrix of test data with the same column names as the training data.

- .approach_score_target
Character string. How should the aggregation of the estimates of the truncated normal distribution for the predictions using OrdPLS/OrdPLSc be done? One of "

*mean*", "*median*" or "*mode*". If "*mean*", the mean of the estimated endogenous indicators is calculated. If "*median*", the mean of the estimated endogenous indicators is calculated. If "*mode*", the maximum empirical density on the intervals defined by the thresholds is used. Defaults to "*mean*".- .sim_points
Integer. How many samples from the truncated normal distribution should be simulated to estimate the exogenous construct scores? Defaults to "

*100*".- .disattenuate
Logical. Should the benchmark predictions be based on disattenuated parameter estimates? Defaults to

`TRUE`

.- .treat_as_continuous
Logical. Should the indicators for the benchmark predictions be treated as continuous? If

`TRUE`

all indicators are treated as continuous and PLS-PM/PLSc is applied. If`FALSE`

OrdPLS/OrdPLSc is applied. Defaults to`TRUE`

.- .approach_score_benchmark
Character string. How should the aggregation of the estimates of the truncated normal distribution be done for the benchmark predictions? Ignored if not OrdPLS or OrdPLSc is used to obtain benchmark predictions. One of "

*mean*", "*median*", "*mode*" or "*round*". If "*round*", the benchmark predictions are obtained using the traditional prediction algorithm for PLS-PM which are rounded for categorical indicators. If "*mean*", the mean of the estimated endogenous indicators is calculated. If "*median*", the mean of the estimated endogenous indicators is calculated. If "*mode*", the maximum empirical density on the intervals defined by the thresholds is used. If`.treat_as_continuous = TRUE`

or if all indicators are on a continuous scale,`.approach_score_benchmark`

is ignored. Defaults to "*round*".- .seed
Integer or

`NULL`

. The random seed to use. Defaults to`NULL`

in which case an arbitrary seed is chosen. Note that the scope of the seed is limited to the body of the function it is used in. Hence, the global seed will not be altered!

An object of class `cSEMPredict`

with print and plot methods.
Technically, `cSEMPredict`

is a
named list containing the following list elements:

`$Actual`

A matrix of the actual values/indicator scores of the endogenous constructs.

`$Prediction_target`

A list containing matrices of the predicted indicator scores of the endogenous constructs based on the target model for each repetition .r. Target refers to procedure used to estimate the parameters in

`.object`

.`$Residuals_target`

A list of matrices of the residual indicator scores of the endogenous constructs based on the target model in each repetition .r.

`$Residuals_benchmark`

A list of matrices of the residual indicator scores of the endogenous constructs based on a model estimated by the procedure given to

`.benchmark`

for each repetition .r.`$Prediction_metrics`

A data frame containing the predictions metrics MAE, RMSE, Q2_predict, the misclassification error rate (MER), the MAPE, the MSE2, Theil's forecast accuracy (U1), Theil's forecast quality (U2), Bias proportion of MSE (UM), Regression proportion of MSE (UR), and disturbance proportion of MSE (UD) (Hora and Campos 2015; Watson and Teelucksingh 2002) .

`$Information`

A list with elements

`Target`

,`Benchmark`

,`Number_of_observations_training`

,`Number_of_observations_test`

,`Number_of_folds`

,`Number_of_repetitions`

, and`Handle_inadmissibles`

.

The predict function implements the procedure introduced by Shmueli et al. (2016)
in the PLS context
known as "PLSPredict" (Shmueli et al. 2019)
including its variants PLScPredcit, OrdPLSpredict and OrdPLScpredict.
It is used to predict the indicator scores of endogenous constructs and to evaluate the out-of-sample predictive power
of a model.
For that purpose, the predict function uses k-fold cross-validation to randomly
split the data into training and test datasets, and subsequently predicts the
values of the test data based on the model parameter estimates obtained
from the training data. The number of cross-validation folds is 10 by default but
may be changed using the `.cv_folds`

argument.
By default, the procedure is not repeated (`.r = 1`

). You may choose to repeat
cross-validation by setting a higher `.r`

to be sure not to have a particular
(unfortunate) split. See Shmueli et al. (2019)
for
details. Typically `.r = 1`

should be sufficient though.

Alternatively, users may supply a test dataset as matrix or a data frame of `.test_data`

with
the same column names as those in the data used to obtain `.object`

(the training data).
In this case, arguments `.cv_folds`

and `.r`

are
ignored and predict uses the estimated coefficients from `.object`

to
predict the values in the columns of `.test_data`

.

In Shmueli et al. (2016)
PLS-based predictions for indicator `i`

are compared to the predictions based on a multiple regression of indicator `i`

on all available exogenous indicators (`.benchmark = "lm"`

) and
a simple mean-based prediction summarized in the Q2_predict metric.
`predict()`

is more general in that is allows users to compare the predictions
based on a so-called target model/specification to predictions based on an
alternative benchmark. Available benchmarks include predictions
based on a linear model, PLS-PM weights, unit weights (i.e. sum scores),
GSCA weights, PCA weights, and MAXVAR weights.

Each estimation run is checked for admissibility using `verify()`

. If the
estimation yields inadmissible results, `predict()`

stops with an error (`"stop"`

).
Users may choose to `"ignore"`

inadmissible results or to simply set predictions
to `NA`

(`"set_NA"`

) for the particular run that failed.

Hora J, Campos P (2015).
“A review of performance criteria to validate simulation models.”
*Expert Systems*, **32**(5), 578--595.
doi:10.1111/exsy.12111
.

Shmueli G, Ray S, Estrada JMV, Chatla SB (2016).
“The Elephant in the Room: Predictive Performance of PLS Models.”
*Journal of Business Research*, **69**(10), 4552--4564.
doi:10.1016/j.jbusres.2016.03.049
.

Shmueli G, Sarstedt M, Hair JF, Cheah J, Ting H, Vaithilingam S, Ringle CM (2019).
“Predictive Model Assessment in PLS-SEM: Guidelines for Using PLSpredict.”
*European Journal of Marketing*, **53**(11), 2322--2347.
doi:10.1108/ejm-02-2019-0189
.

Watson PK, Teelucksingh SS (2002).
*A practical introduction to econometric methods: Classical and modern*.
University of West Indies Press, Mona, Jamaica.

```
### Anime example taken from https://github.com/ISS-Analytics/pls-predict/
# Load data
data(Anime) # data is similar to the Anime.csv found on
# https://github.com/ISS-Analytics/pls-predict/ but with irrelevant
# columns removed
# Split into training and data the same way as it is done on
# https://github.com/ISS-Analytics/pls-predict/
set.seed(123)
index <- sample.int(dim(Anime)[1], 83, replace = FALSE)
dat_train <- Anime[-index, ]
dat_test <- Anime[index, ]
# Specify model
model <- "
# Structural model
ApproachAvoidance ~ PerceivedVisualComplexity + Arousal
# Measurement/composite model
ApproachAvoidance =~ AA0 + AA1 + AA2 + AA3
PerceivedVisualComplexity <~ VX0 + VX1 + VX2 + VX3 + VX4
Arousal <~ Aro1 + Aro2 + Aro3 + Aro4
"
# Estimate (replicating the results of the `simplePLS()` function)
res <- csem(dat_train,
model,
.disattenuate = FALSE, # original PLS
.iter_max = 300,
.tolerance = 1e-07,
.PLS_weight_scheme_inner = "factorial"
)
# Predict using a user-supplied training data set
pp <- predict(res, .test_data = dat_test)
#> Warning: The following warning occured in the `predict()` function:
#> Disattenuation is not applicable to benchmark `lm` and ignored.
pp
#> ________________________________________________________________________________
#> ----------------------------------- Overview -----------------------------------
#>
#> Number of obs. training = 100
#> Number of obs. test = 83
#> Number of cv folds = NA
#> Number of repetitions = 1
#> Handle inadmissibles = stop
#> Estimator target = 'PLS-PM'
#> Estimator benchmark = 'lm'
#> Disattenuation target = 'FALSE'
#> Disattenuation benchmark = 'FALSE'
#> Approach to predict = 'earliest'
#>
#> ------------------------------ Prediction metrics ------------------------------
#>
#>
#> Name MAE target MAE benchmark RMSE target RMSE benchmark Q2_predict
#> AA0 1.2125 1.1621 1.5575 1.5045 0.4625
#> AA1 1.5319 1.5711 1.9005 1.9829 0.2794
#> AA2 0.9891 0.9804 1.3993 1.4029 0.4396
#> AA3 1.0564 1.0472 1.4434 1.4787 0.3656
#> ________________________________________________________________________________
### Compute prediction metrics ------------------------------------------------
res2 <- csem(Anime, # whole data set
model,
.disattenuate = FALSE, # original PLS
.iter_max = 300,
.tolerance = 1e-07,
.PLS_weight_scheme_inner = "factorial"
)
# Predict using 10-fold cross-validation
if (FALSE) {
pp2 <- predict(res, .benchmark = "lm")
pp2
## There is a plot method available
plot(pp2)}
### Example using OrdPLScPredict -----------------------------------------------
# Transform the numerical indicators into factors
if (FALSE) {
data("BergamiBagozzi2000")
data_new <- data.frame(cei1 = as.ordered(BergamiBagozzi2000$cei1),
cei2 = as.ordered(BergamiBagozzi2000$cei2),
cei3 = as.ordered(BergamiBagozzi2000$cei3),
cei4 = as.ordered(BergamiBagozzi2000$cei4),
cei5 = as.ordered(BergamiBagozzi2000$cei5),
cei6 = as.ordered(BergamiBagozzi2000$cei6),
cei7 = as.ordered(BergamiBagozzi2000$cei7),
cei8 = as.ordered(BergamiBagozzi2000$cei8),
ma1 = as.ordered(BergamiBagozzi2000$ma1),
ma2 = as.ordered(BergamiBagozzi2000$ma2),
ma3 = as.ordered(BergamiBagozzi2000$ma3),
ma4 = as.ordered(BergamiBagozzi2000$ma4),
ma5 = as.ordered(BergamiBagozzi2000$ma5),
ma6 = as.ordered(BergamiBagozzi2000$ma6),
orgcmt1 = as.ordered(BergamiBagozzi2000$orgcmt1),
orgcmt2 = as.ordered(BergamiBagozzi2000$orgcmt2),
orgcmt3 = as.ordered(BergamiBagozzi2000$orgcmt3),
orgcmt5 = as.ordered(BergamiBagozzi2000$orgcmt5),
orgcmt6 = as.ordered(BergamiBagozzi2000$orgcmt6),
orgcmt7 = as.ordered(BergamiBagozzi2000$orgcmt7),
orgcmt8 = as.ordered(BergamiBagozzi2000$orgcmt8))
model <- "
# Measurement models
OrgPres =~ cei1 + cei2 + cei3 + cei4 + cei5 + cei6 + cei7 + cei8
OrgIden =~ ma1 + ma2 + ma3 + ma4 + ma5 + ma6
AffJoy =~ orgcmt1 + orgcmt2 + orgcmt3 + orgcmt7
AffLove =~ orgcmt5 + orgcmt 6 + orgcmt8
# Structural model
OrgIden ~ OrgPres
AffLove ~ OrgIden
AffJoy ~ OrgIden
"
# Estimate using cSEM; note: the fact that indicators are factors triggers OrdPLSc
res <- csem(.model = model, .data = data_new[1:250,])
summarize(res)
# Predict using OrdPLSPredict
set.seed(123)
pred <- predict(
.object = res,
.benchmark = "PLS-PM",
.test_data = data_new[(251):305,],
.treat_as_continuous = TRUE, .approach_score_target = "median"
)
pred
round(pred$Prediction_metrics[, -1], 4)}
```