README.Rmd

---
title: Multi-Study Factor Regression (MSRF)
author: 
- Roberta De Vito
- Alejandra Avalos-Pacheco
- Jörg Schantz
---

Fit the Multi-Study Factor Regression model via the [ECM algorithm](https://doi.org/10.1002/sim.70108).

## Fitting the MSFR model via the ECM Algorithm

The following example illustrates how to fit the MSFR model via the ECM Algorithm, 
using a data set generating from a simulation scenario. 

### Getting the data

```{r help2, eval = FALSE}
library(MSFR)
data(Scenario1_MSFR)
```

### Obtaining suitable starting values for model parameters
Then we get inizialization for model parameters, with k=3 common
factors and j_s=[1,1] study-specific factors for two studies (S=2).

```{r, starting values, eval = FALSE}
start_value <- start_msfa(X_s, B_s, k, j_s, constraint = "block_lower2", method = "adhoc")
```

### Fitting the model via ECM
Now we can proceed for estimating the model parameters via the ECM algorithm

```{r get estimate, eval = FALSE}
ECM_MSFR <- ecm_msfr(X_s, B_s, start=start_value,  nIt = 10000, trace = FALSE)
```

The estimated matrix of common loadings
```{r get common, eval = FALSE}
Phi <- ECM_MSFR$Phi
```

The estimated matrix of study-specific loadings
```{r get spec, eval = FALSE}
Lambda_1 <- ECM_MSFR$Lambda_s[[1]]
Lambda_2 <- ECM_MSFR$Lambda_s[[2]]
```

The estimated idiosyncratic error matrices

```{r get errors, eval = FALSE}
Psi_1 <- ECM_MSFR$Psi_s[[1]]
Psi_2 <- ECM_MSFR$Psi_s[[2]]
```


The estimated matrix of regression coefficients for covariates effect can be visualized
```{r get cov, eval = FALSE}
Beta <- ECM_MSFR$Beta
```

### Visualisation of the each output matrices
```{r, eval = FALSE}
heat_plot(Phi)
heat_plot(Lambda_1)
heat_plot(Lambda_2)
heat_plot(Psi_1)
heat_plot(Psi_2)
heat_plot(Beta)
```