Statistical Approaches for Highly Skewed Data: Evaluating Relations

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Statistical Approaches for Highly Skewed Data:

"Non-Suicidal Self-injury Department of Psychology, University of California, Riverside : Clinical phenomena often feature skewed distributions with an overabundance of

Method: College students

N= 2,651; 64.2% female; 85.2% nonwhite) completed the Child Abuse and Trauma Scale ated Poisson (ZIP) and negative-binomial zero-inated (NBZI) regression tdistribution to model NSSI skewness.Results: Child maltreatment was signicantly ated -tmodel.Conclusions: Thesendings ated models rather than transformation approaches tdistribution has been used to model non-clinicaldata, this study suggests that the skew-tapproach may not be well- clinicaldata. c assumptions relevant true regression model for the population; Osborne & Waters, estimatedregression model; Weisberg, "s body tissue without suicidal intent; Journal of Clinical Child & Adolescent Psychology, 49(02), 1-15, 2020

The Phenomenology of NSSI

Over the past 20 years, NSSI has emerged as a prominent -25 (Whitlock, Eckenrode, & Silverman, rms signicant rates of NSSI among notendorse NSSI far exceeds the num- cant psychological distress and ni et al.,

Contemporary Approaches to Address Distributional

Data skewness refers to a lack of symmetry in the data ecting ecting an excess of t by minimizing the sum dence intervals. In a series of simulated -tdistribution, directly model skew-

Variable Transformation Approaches

Transforming observed data is the most common

natural log, square-root, and inversetransformations. Moreover, multiple transforma- t indices (e.g., RMSEA, 'sf 2 c reason not to, such as when using non-parametric

2GONZALEZ-BLANKS ET AL.

Zero-Inflated Approaches

Zero-inated models canbe used to analyze data whenthere ated models yield two parameters, one that estimates ated Poisson (ZIP; Lambert, ated (NBZI; Minami, Lennert- andfor a greater level of overdis- dence intervals from the NBZI model are likely to be ated approaches require t -2017 -2017

Skew-t Distribution Approach

Although Azzalini (

tdistribution), analytic software has only recently advanced rst to our knowledge to apply this approach in the -tdistribution accounts for skewness (and kur- -tdistribution will equal thetdistribution nity (Asparouhov & Muthén, cant advantage of the skew- tapproach is that skewness is modeled using predictors -2017

Summary

Individual approachesfordealingwith data skewnesshave atedapproachesthataddresstheoverabun- 3

The Current Study

This investigation evaluated raw, transformation, zero- ated, and skew-tdistribution methods for dealing with 'self-reported histories of child maltreatment and tdistribution. Each approach for t indices were evaluated to select the tting model within each approach. This model was ated models would yield the most accurate NSSI

METHOD

The present sample included 2,651 undergraduate students M age

SD= 1.196) at a large University in the

c countries of origin were not available.

Procedures

Participants were recruited from introductory psychology c reference to the potentially triggering nature of the dentiality limitations perti- ed by a code number cult life

Measures

Non-Suicidal Self-Injury (NSSI)

Participants completed the Functional Assessment of

0 times), 1 (1 time), 2 (2 times), 3 (3-5 times), 4

6-10 times), 5 (11-20 times), and 6 (>20 times). For these

ned as the sum of ed as

4GONZALEZ-BLANKS ET AL.

Child Maltreatment

The Child Abuse and Trauma Scale (CATS) includes 38 "Did your parents ever hit or beat you when you did not ""Did your relationship with your parents ever "). Items were rated on ave- never)to4(always) and composited to fl= .916). The CATS

Data Analytic Plan

Analysis Software

Data preparation was conducted utilizing IMB SPSS 26 'sMCARtest( -2017

Data Preparation

Prior to analyses, all predictors and continuous covariates 's age and NSSI, as well as skewness, p<.001,

Data Analysis and Missingness

Data were missing on age (3.2%), child maltreatment 's( 2 p= .442,

Model Evaluation

Allvariableswerecenteredtoreducemulticollinearity,since dence

Model Fitting Approach 1.Modelt was assessed

t chi-squares, the comparative t index (CFI > .90), the Tucker-Lewis Index (TLI > .90), the

TABLE 1

NMSDSkewness Kurtosis

NSSI (raw) 2524 1.782 2.145 3.228 11.109

0.595

Note. NSSI = Non-Suicidal Self-Injury.

t. ndings. 5 Failure to meet criteria on one or morefit indices was indi- fit.

Model Fitting Approach 2.Information measures

fit when the abovefit indices were unavail- 's information criterion (AIC), fitting for all model approaches.

Model Comparisons

Traditional methods (e.g., chi-square differences) were

Model Approaches

The regression model evaluated the effect of child d

NSSI¼

0 1

CATSþ

2

SQRTþ

3

GENDERþ

4 RACE

Raw Regression Approach (A).The raw NSSI vari-

Transformation Approaches (B).NSSI was trans-

Zero-Inαated Regression Model Approaches

The ZIP (Model C.1) and NBZI (Model C.2) regres-

d

ðNSSI

#1

Þand the

d

ðNSSI

0

Þ. The ZIP model used

Skew-t Distribution Approach (D).The skew-t

distribution approach adds a skew scaling weight when

RESULTS

Out of the 2,651 participants, 16.3% reported having engaged ficant main effects '= .985,p< .001) and ethni- '= .970,p< .001), as well as for their '=.987,p< .001). Between-subjects ficant gender differences in participant ficant differences in all study variables across ethnic- ficant gender*ethnicity-race interaction for maltreat- ficant gender*ethnicity-race interaction for NSSI, ficantly by gender. At the bivariate r=.239,p< .001), but age was not significantly related to

Model Fitting

Tables 4 fitting indices for all

Statistical Approaches for Highly Skewed Data:

"Non-Suicidal Self-injury Department of Psychology, University of California, Riverside : Clinical phenomena often feature skewed distributions with an overabundance of

Method: College students

N= 2,651; 64.2% female; 85.2% nonwhite) completed the Child Abuse and Trauma Scale ated Poisson (ZIP) and negative-binomial zero-inated (NBZI) regression tdistribution to model NSSI skewness.Results: Child maltreatment was signicantly ated -tmodel.Conclusions: Thesendings ated models rather than transformation approaches tdistribution has been used to model non-clinicaldata, this study suggests that the skew-tapproach may not be well- clinicaldata. c assumptions relevant true regression model for the population; Osborne & Waters, estimatedregression model; Weisberg, "s body tissue without suicidal intent; Journal of Clinical Child & Adolescent Psychology, 49(02), 1-15, 2020

The Phenomenology of NSSI

Over the past 20 years, NSSI has emerged as a prominent -25 (Whitlock, Eckenrode, & Silverman, rms signicant rates of NSSI among notendorse NSSI far exceeds the num- cant psychological distress and ni et al.,

Contemporary Approaches to Address Distributional

Data skewness refers to a lack of symmetry in the data ecting ecting an excess of t by minimizing the sum dence intervals. In a series of simulated -tdistribution, directly model skew-

Variable Transformation Approaches

Transforming observed data is the most common

natural log, square-root, and inversetransformations. Moreover, multiple transforma- t indices (e.g., RMSEA, 'sf 2 c reason not to, such as when using non-parametric

2GONZALEZ-BLANKS ET AL.

Zero-Inflated Approaches

Zero-inated models canbe used to analyze data whenthere ated models yield two parameters, one that estimates ated Poisson (ZIP; Lambert, ated (NBZI; Minami, Lennert- andfor a greater level of overdis- dence intervals from the NBZI model are likely to be ated approaches require t -2017 -2017

Skew-t Distribution Approach

Although Azzalini (

tdistribution), analytic software has only recently advanced rst to our knowledge to apply this approach in the -tdistribution accounts for skewness (and kur- -tdistribution will equal thetdistribution nity (Asparouhov & Muthén, cant advantage of the skew- tapproach is that skewness is modeled using predictors -2017

Summary

Individual approachesfordealingwith data skewnesshave atedapproachesthataddresstheoverabun- 3

The Current Study

This investigation evaluated raw, transformation, zero- ated, and skew-tdistribution methods for dealing with 'self-reported histories of child maltreatment and tdistribution. Each approach for t indices were evaluated to select the tting model within each approach. This model was ated models would yield the most accurate NSSI

METHOD

The present sample included 2,651 undergraduate students M age

SD= 1.196) at a large University in the

c countries of origin were not available.

Procedures

Participants were recruited from introductory psychology c reference to the potentially triggering nature of the dentiality limitations perti- ed by a code number cult life

Measures

Non-Suicidal Self-Injury (NSSI)

Participants completed the Functional Assessment of

0 times), 1 (1 time), 2 (2 times), 3 (3-5 times), 4

6-10 times), 5 (11-20 times), and 6 (>20 times). For these

ned as the sum of ed as

4GONZALEZ-BLANKS ET AL.

Child Maltreatment

The Child Abuse and Trauma Scale (CATS) includes 38 "Did your parents ever hit or beat you when you did not ""Did your relationship with your parents ever "). Items were rated on ave- never)to4(always) and composited to fl= .916). The CATS

Data Analytic Plan

Analysis Software

Data preparation was conducted utilizing IMB SPSS 26 'sMCARtest( -2017

Data Preparation

Prior to analyses, all predictors and continuous covariates 's age and NSSI, as well as skewness, p<.001,

Data Analysis and Missingness

Data were missing on age (3.2%), child maltreatment 's( 2 p= .442,

Model Evaluation

Allvariableswerecenteredtoreducemulticollinearity,since dence

Model Fitting Approach 1.Modelt was assessed

t chi-squares, the comparative t index (CFI > .90), the Tucker-Lewis Index (TLI > .90), the

TABLE 1

NMSDSkewness Kurtosis

NSSI (raw) 2524 1.782 2.145 3.228 11.109

0.595

Note. NSSI = Non-Suicidal Self-Injury.

t. ndings. 5 Failure to meet criteria on one or morefit indices was indi- fit.

Model Fitting Approach 2.Information measures

fit when the abovefit indices were unavail- 's information criterion (AIC), fitting for all model approaches.

Model Comparisons

Traditional methods (e.g., chi-square differences) were

Model Approaches

The regression model evaluated the effect of child d

NSSI¼

0 1

CATSþ

2

SQRTþ

3

GENDERþ

4 RACE

Raw Regression Approach (A).The raw NSSI vari-

Transformation Approaches (B).NSSI was trans-

Zero-Inαated Regression Model Approaches

The ZIP (Model C.1) and NBZI (Model C.2) regres-

d

ðNSSI

#1

Þand the

d

ðNSSI

0

Þ. The ZIP model used

Skew-t Distribution Approach (D).The skew-t

distribution approach adds a skew scaling weight when

RESULTS

Out of the 2,651 participants, 16.3% reported having engaged ficant main effects '= .985,p< .001) and ethni- '= .970,p< .001), as well as for their '=.987,p< .001). Between-subjects ficant gender differences in participant ficant differences in all study variables across ethnic- ficant gender*ethnicity-race interaction for maltreat- ficant gender*ethnicity-race interaction for NSSI, ficantly by gender. At the bivariate r=.239,p< .001), but age was not significantly related to

Model Fitting

Tables 4 fitting indices for all