Psychologists often use scales composed of multiple items to measure underlying constructs, such as wellbeing, depression, and personality traits. Missing data often occurs at the itemlevel. If variables in the dataset can account for the missingness, the data is missing at random (MAR). Modern missing data approaches can deal with MAR missing data effectively, but existing analytical approaches cannot accommodate itemlevel missing data. A very common practice in psychology is to average all available items to produce scale means when there is missing data. This approach, called availablecase maximum likelihood (ACML) may produce biased results in addition to incorrect standard errors. Another approach is scalelevel full information maximum likelihood (SLFIML), which treats the whole scale as missing if even one item is missing. SLFIML is inefficient and prone to bias. A new analytical approach, called the twostage maximum likelihood approach (TSML), was recently developed as an alternative by Savalei and Rhemtulla (2017). The original work showed that the method outperformed ACML and SLFIML in structural equation models with parcels. Our current study examines the performance of ACML, SLFIML, and TSML in the context of bivariate regression.
Research
ItemLevel Missing Data

Investigators: Bill Chen and Dr. Victoria Savalei
Measurement Invariance

Investigators: Jordan Brace and Dr. Victoria Savalei
Measurement invariance is the property of psychometric instruments indicating that they perform identically when applied to different populations. When measurement invariance does not hold between populations, comparing scores of individuals from different populations (e.g., in crosscultural research, or using a threshold for diagnosis) is inappropriate. Our research on this topic focuses on evaluating methods for testing measurement invariance, particularly when data are nonnormal, as well as meaningfuilly quantifying the impact of an absence of measurement invariance in applications of psychometric instruments.
Bayesian Statistics in Social Sciences

Investigators: Bill Chen and Dr. Victoria Savalei
In recent years, some researchers have advocated a wider adoption of Bayesian data analysis in social sciences. The usual arguments state that significance testing is unintuitive and prone to frequent misuse, while Bayesian statistics overcomes these problems. We aim to empirically investigate how social scientists would apply some of these Bayesian techniques, and whether there may be potential pitfalls that we need to be more aware of.
Format of Psychological Scales

Investigators: Cathy Xijuan Zhang and Dr. Victoria Savalei
Undergraduate Helpers: Bernice Liang, Yu Luo, Ramsha Noor and Kurtis Stewart
The traditional Likert format scale usually contains both positively worded (PW) items and reverse worded (RW) items. The main rationale for including RW items on scales is to for control acquiescence bias, which is the tendency for respondents to endorse the item regardless of its content (Ray, 1983). However, many researchers have questioned the benefit of including RW items in scales (e.g., Sonderen, Sanderman & Coyne, 2013). First, if the tendency to engage in acquiescence bias is an individual difference variable, then it will always contaminate the covariance structure of the data. Second, some RW items may cause confused and lead to errors due to carelessness among some respondents. Finally, RW items may also create method effects that represent a consistent behavioral trait, such as fear of negative evaluation (e.g., DiStefano & Molt, 2006), and these method effects may cause the scales to have lower validity and reliability (e.g., Rodebaugh et al., 2011; Roszkowski & Soven, 2010). Unlike scales in the Likert format, scales in the Expanded format do not contain RW items and thus do not have the problems associated with RW items. In the Expanded format, a full sentence replaces each of the response option in the Likert format. For instance, an item from the Rosenberg SelfEsteem Scale (RSES) that reads
On the whole, I am satisfied with myself.
and that has four response options (i.e.,Strongly disagree
,Somewhat disagree
,Somewhat agree
, andStrongly agree
) would be written in the Expanded format as follows : On the whole, I am very satisfied with myself.
 On the whole, I am satisfied with myself.
 On the whole, I am disappointed with myself.
 On the whole, I am very disappointed with myself.
I am not happy
misread asI am happy
).
Bootstrap Fit Indices

Investigators: Cathy Xijuan Zhang and Dr. Victoria Savalei
Bootstrapping approximate fit indices in structural equation modeling (SEM) is of great importance because most fit indices do not have tractable analytic distributions. Modelbased bootstrap, which has been proposed to obtain the distribution of the model chisquare statistic under the null hypothesis (Bollen & Stine, 1992), is not theoretically appropriate for obtaining confidence intervals for fit indices because it assumes the null is exactly true. On the other hand, naive bootstrap is not expected to work well for those fit indices that are based on the chisquare statistic, such as the RMSEA and the CFI, because sample noncentrality is a biased estimate of the population noncentrality. In this article we argue that a recently proposed bootstrap approach due to Yuan, Hayashi, and Yanagihara (YHY; 2007) is ideal for bootstrapping fit indices such as RMSEA and CFI that are based on the chisquare. This method transforms the data so that the parent population has the population noncentrality parameter equal to the estimated noncentrality in the original sample. Our lab is investigating the performance of the YHY bootstrap and the naive bootstrap for four indices: RMSEA, CFI, GFI, and SRMR. We are finding that for RMSEA and CFI, the confidence intervals (CIs) under the YHY bootstrap have relatively good coverage rates for all conditions whereas the CIs under the naïve bootstrap have very low coverage rates when the fitted model had large degrees of freedom.
Impact of Reverse Wording

Investigators: Cathy Xijuan Zhang, Ramsha Noor and Victoria Savalei
Undergraduate Helpers: Kurtis Stewart
Reverse wording is frequently employed across a variety of psychological scales to reduce or eliminate acquiescence bias, but there is rising concern about its harmful effects, one being the ability to contaminate the covariance structure of the scale. Therefore, results obtained via traditional covariance analyses may be distorted. Our lab examines the impact of reverse wording on the factor structure of the abbreviated 18item Need for Cognition (NFC) scale using confirmatory and exploratory factor analysis. Data is fit to four previously developed models, including a unidimensional single factor model, a two factor model distinguishing between items of positive polarity and those of negative polarity, and two twofactor models, each with one all encompassing factor and one method factor. The NFC scale is modified to form three revised versions, varying from no reverse worded items to all reverse worded items. The original scale and revised versions are each fit to the four different models in hopes to gain further insight into not only the dimensionality of the scale, but also the effect of reverse wording on the factor structure. Our current results show that degree and type of reverse wording differentially impacts the factor structure and functionality of the NFC scale.