# MTMM: Multi Trait Multi Method Matrix In multicon: Multivariate Constructs

## Description

Returns the summary results from a multi-trait multi-method correlation matrix including the average correlations for Same Trait-Different Method, Same Method-Different Trait, and Different Method-Different Trait.

## Usage

 `1` ```MTMM(x, traits, methods) ```

## Arguments

 `x` A data.frame organized such that each column represents the ratings for each Trait-Method combination. The columns must be ordered in sets such that the first set is the first trait rated by each method, followed by the second trait rated by each method (in the same order), and so on. `traits` An integer indicating the total number of different traits rated. `methods` An integer indicating the total number of methods used.

## Details

Multi-trait Multi-method matrices are often used examine the validity of the construct(s) under investigation. That is, if different methods agree about a target's standing on a trait, it is more likely that the trait itself is valid. However, such agreement must be compared with agreement about different targets using the same method (method effects), which must in turn be compared with agreement about different targets using different methods (i.e., the general similarity of targets). This function returns all three such values: The average agreement about targets on the given traits using different methods, the average agreement about different targets using the same methods (method effects), and the average agreement about different targets using different methods (baseline agreement).

## Value

 `SameTrait ` The average correlation for the Same Traits rated by Different Methods `SameMethod ` The average correlation for the Same Methods used to rate the Different Traits `DiffDiff` The average correlation for the Different Traits rated by Different Methods

## Author(s)

Ryne A. Sherman

`inner.outer`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10``` ``` # We can generate some random data by first creating a population correlation matrix sig <- matrix(c(1.00,.4,.6,.05,.1,-.05,.4,1.00,.5,.08, -.02,.03,.6,.5,1.00,.09,.1,-.07,.05,.08,.09,1.00,.6,.7,.1,-.02,.1,.6, 1.00,.5,-.05,.03,-.07,.7,.5,1.00), ncol=6, byrow=TRUE) sig library(mvtnorm) # Now create random data based on this population matrix d <- rmvnorm(100, sigma=sig) #Now use MTMM on this data.frame indicating that there are 2 traits and 3 methods. MTMM(d, 2, 3) ```

### Example output

```Loading required package: psych
[,1]  [,2]  [,3] [,4]  [,5]  [,6]
[1,]  1.00  0.40  0.60 0.05  0.10 -0.05
[2,]  0.40  1.00  0.50 0.08 -0.02  0.03
[3,]  0.60  0.50  1.00 0.09  0.10 -0.07
[4,]  0.05  0.08  0.09 1.00  0.60  0.70
[5,]  0.10 -0.02  0.10 0.60  1.00  0.50
[6,] -0.05  0.03 -0.07 0.70  0.50  1.00
SameTrait SameMethod  DiffDiff
Results 0.5795363 0.05405483 0.1212359
```

multicon documentation built on May 2, 2019, 3:18 a.m.