Calculate the conditional Mahalanobis distance for any variables.

```
cond_maha(
data,
R,
v_dep,
v_ind = NULL,
v_ind_composites = NULL,
mu = 0,
sigma = 1,
use_sample_stats = FALSE,
label = NA
)
```

- data
Data.frame with the independent and dependent variables. Unless mu and sigma are specified, data are assumed to be z-scores.

- R
Correlation among all variables.

- v_dep
Vector of names of the dependent variables in your profile.

- v_ind
Vector of names of independent variables you would like to control for.

- v_ind_composites
Vector of names of independent variables that are composites of dependent variables

- mu
A vector of means. A single value means that all variables have the same mean.

- sigma
A vector of standard deviations. A single value means that all variables have the same standard deviation

- use_sample_stats
If TRUE, estimate R, mu, and sigma from data. Only complete cases are used (i.e., no missing values in v_dep, v_ind, v_ind_composites).

- label
optional tag for labeling output

a list with the conditional Mahalanobis distance

`dCM`

= Conditional Mahalanobis distance`dCM_df`

= Degrees of freedom for the conditional Mahalanobis distance`dCM_p`

= A proportion that indicates how unusual this profile is compared to profiles with the same independent variable values. For example, if`dCM_p`

= 0.88, this profile is more unusual than 88 percent of profiles after controlling for the independent variables.`dM_dep`

= Mahalanobis distance of just the dependent variables`dM_dep_df`

= Degrees of freedom for the Mahalanobis distance of the dependent variables`dM_dep_p`

= Proportion associated with the Mahalanobis distance of the dependent variables`dM_ind`

= Mahalanobis distance of just the independent variables`dM_ind_df`

= Degrees of freedom for the Mahalanobis distance of the independent variables`dM_ind_p`

= Proportion associated with the Mahalanobis distance of the independent variables`v_dep`

= Dependent variable names`v_ind`

= Independent variable names`v_ind_singular`

= Independent variables that can be perfectly predicted from the dependent variables (e.g., composite scores)`v_ind_nonsingular`

= Independent variables that are not perfectly predicted from the dependent variables`data`

= data used in the calculations`d_ind`

= independent variable data`d_inp_p`

= Assuming normality, cumulative distribution function of the independent variables`d_dep`

= dependent variable data`d_dep_predicted`

= predicted values of the dependent variables`d_dep_deviations = d_dep - d_dep_predicted`

(i.e., residuals of the dependent variables)`d_dep_residuals_z`

= standardized residuals of the dependent variables`d_dep_cp`

= conditional proportions associated with standardized residuals`d_dep_p`

= Assuming normality, cumulative distribution function of the dependent variables`R2`

= Proportion of variance in each dependent variable explained by the independent variables`SEE`

= Standard error of the estimate for each dependent variable`ConditionalCovariance`

= Covariance matrix of the dependent variables after controlling for the independent variables`distance_reduction = 1 - (dCM / dM_dep)`

(Degree to which the independent variables decrease the Mahalanobis distance of the dependent variables. Negative reductions mean that the profile is more unusual after controlling for the independent variables. Returns 0 if`dM_dep`

is 0.)`variability_reduction = 1 - sum((X_dep - predicted_dep) ^ 2) / sum((X_dep - mu_dep) ^ 2)`

(Degree to which the independent variables decrease the variability the dependent variables (`X_dep`

). Negative reductions mean that the profile is more variable after controlling for the independent variables. Returns 0 if`X_dep == mu_dep`

)`mu`

= Variable means`sigma`

= Variable standard deviations`d_person`

= Data frame consisting of Mahalanobis distance data for each person`d_variable`

= Data frame consisting of variable characteristics`label`

= label slot

```
library(unusualprofile)
library(simstandard)
m <- "
Gc =~ 0.85 * Gc1 + 0.68 * Gc2 + 0.8 * Gc3
Gf =~ 0.8 * Gf1 + 0.9 * Gf2 + 0.8 * Gf3
Gs =~ 0.7 * Gs1 + 0.8 * Gs2 + 0.8 * Gs3
Read =~ 0.66 * Read1 + 0.85 * Read2 + 0.91 * Read3
Math =~ 0.4 * Math1 + 0.9 * Math2 + 0.7 * Math3
Gc ~ 0.6 * Gf + 0.1 * Gs
Gf ~ 0.5 * Gs
Read ~ 0.4 * Gc + 0.1 * Gf
Math ~ 0.2 * Gc + 0.3 * Gf + 0.1 * Gs"
# Generate 10 cases
d_demo <- simstandard::sim_standardized(m = m, n = 10)
# Get model-implied correlation matrix
R_all <- simstandard::sim_standardized_matrices(m)$Correlations$R_all
cond_maha(data = d_demo,
R = R_all,
v_dep = c("Math", "Read"),
v_ind = c("Gf", "Gs", "Gc"))
#> Conditional Mahalanobis Distance = 1.3222, df = 2, p = 0.5828 Conditional Mahalanobis Distance = 1.0531, df = 2, p = 0.4256 Conditional Mahalanobis Distance = 0.2780, df = 2, p = 0.0379 Conditional Mahalanobis Distance = 0.6676, df = 2, p = 0.1998 Conditional Mahalanobis Distance = 0.9099, df = 2, p = 0.3390 Conditional Mahalanobis Distance = 0.0803, df = 2, p = 0.0032 Conditional Mahalanobis Distance = 0.9747, df = 2, p = 0.3782 Conditional Mahalanobis Distance = 0.8846, df = 2, p = 0.3238 Conditional Mahalanobis Distance = 2.7419, df = 2, p = 0.9767 Conditional Mahalanobis Distance = 0.9059, df = 2, p = 0.3366
```