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\title{The Short Maximization Inventory}

\author{
Michal Ďuriník\thanks{Faculty of Economics and Administration, Masaryk
University; Macquarie Graduate School of Management}
\and
Jakub Procházka\thanks{Faculty of Social Studies and Faculty of Economics and
Administration, Masaryk University}
\and
Hynek Cígler\thanks{Faculty of Social Studies, Masaryk University}
}

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\newcommand{\jhead}{Judgment and Decision Making, Vol.~13, No.~1}
\newcommand{\jdate}{January 2018}
\pagestyle{myheadings} \markright{\protect\small \href{\jref}{\jhead}, \jdate \hfill The Short Maximization Inventory \qquad}
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\href{\jref}{\jhead}, \jdate, pp.\ 123-136
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\begin{onecolabstract}
%\end{latexonly}
  We developed the Short Maximization Inventory (SMI) by shortening
  the Maximization Inventory (Turner, Rim, Betz \& Nygren, 2012) from
  34 items to 15 items. Using the Item Response Theory framework, we
  identified and removed the items of the Maximization Inventory that
  contributed least to the performance of the original scale. The
  construct validity assessed for SMI is similar to the full MI and is
  in line with the predictions from the literature: the Satisficing
  subscale is positively related to the indices of well-being, while
  the Decision Difficulty and Alternative Search subscales are
  negatively related to well-being. The new scale retains the good
  psychometric properties of the original scale. Furthermore, its
  brevity allows researchers to use the scale in studies in which
  maximization is not the primary focus.  Although the SMI lacks the
  ``High Standards'' subscale, as did the original MI, we believe that
  SMI is a step towards developing a reliable and conceptually sound
  measure of maximizing that can be used in various research designs.

\smallskip
\noindent
Keywords: maximization, Maximization Inventory, scale shortening, Short Maximization Inventory 
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{\renewcommand{\thefootnote}{}

\footnotetext{

We wish to thank the editor and the reviewers for the
insightful and valuable comments they provided. This paper is part of
the Masaryk University Specific Research Project MUNI/A/1021/2015.
While finishing this paper, Michal Ďuriník was a holder of Macquarie
University Research Excellence Scholarship.

Copyright: \copyright\ 2018.
The authors license this article under the terms of the
\href{http://creativecommons.org/licenses/by/3.0/}{Creative Commons
  Attribution 3.0 License.}
}}

\saythanks

\section{Introduction}

In economics and other social sciences, humans are often modeled as
\textit{homo }\textit{economicus}\textit{.} Homo economicus is an
all-knowing individual who is flawless in calculating expected
utilities from individual alternatives and choosing the one that
provides the highest utility. Homo economicus \textit{maximizes.} Simon
(1955), however, argues that we are often unable to fulfill this goal
of perfect optimization. Instead, we \textit{satisfice}: we choose
options that meet a certain threshold of acceptability. When our
sub-perfect knowledge and abilities prevent us from opting for the
best, we resort to choosing what is “good enough”.

Half a century later, Schwartz, Ward, Monterosso, Lyubomirsky, White
and Lehman (2002) revisited Simon’s work and proposed maximizing to be
a stable personality trait. According to Schwartz et al., each
individual falls somewhere on a continuous scale between being a
Maximizer (one who tries to find the best of all alternatives) and a
Satisficer (one who is comfortable selecting a “good enough”
alternative). Nenkov, Morrin, Ward, Hulland and Schwartz (2008) later
proposed that maximizing has three dimensions: Decision Difficulty
(the extent to which one experiences difficulty selecting from a range
of options), Alternative Search (the tendency to exert effort and time
exploring available alternatives) and High Standards (the tendency to
hold high standards for oneself and one’s choices).  Recently, Cheek
and Schwartz (2016) proposed maximizing to have two components: the
goal of choosing the best and the strategy of alternative search.

Extensive literature has found that maximizers are more likely than
satisficers to report low self-esteem (Schwartz et al., 2002) and less
likely to feel happy (Larsen \& McKibban, 2008; Polman, 2010; Schwartz
et al., 2002) and to be satisfied with their lives (Dahling \&
Thompson, 2012; Schwartz et al., 2002). Maximization has also been
linked to depression (Schwartz et al., 2002), regret (Moyano-Díaz,
Martínez-Molina \& Ponce, 2014; Schwartz et al., 2002), ruminating on
past events (Paivandy, Bullock, Reardon \& Kelly, 2008) and other
maladaptive traits and behaviors (see Cheek \& Schwartz, 2016, for a
more extensive list).

The results mentioned above were collected using the 13-item
unidimensional Maximization Scale (MS; Schwartz et al., 2002). MS is
the first and most widely used maximization measure, but it has
received significant criticism. An item response analysis conducted by
Rim, Turner, Betz and Nygren (2011), together with previous classical
test theory analyses (e.g., Diab, Gillespie \& Highhouse, 2008;
Giacopelli, Simpson, Dalal, Randoplh \& Holland, 2013;
Nenkov et al., 2008), found MS to have poor psychometric properties.
The main points of criticism towards MS are its composite scoring
(although analyses indicate it possesses a three-factor structure of
Alternative Search, Decision Difficulty, and High Standards); weak
internal consistency (Cronbach’s alpha at the lower bound of
acceptability for use in research); and the presence of items that are
either conceptually too distant from the construct of maximizing (e.g.,
“I often fantasize about living in ways that are quite different from
my actual life”) or focus on overly specific behaviors (e.g., “Renting
videos is really difficult. I’m always struggling to pick the best
one”). In addition, Rim et al.\ (2011) note that satisficing in MS is
measured only indirectly, through a lack of maximizing, and they argue
that a direct measure of satisficing could be a useful contribution.

Since the publication of MS (Schwartz et al., 2002), the scale has been
shortened (Nenkov et al., 2008) and modified (Lai, 2010; Weinhardt,
Morse, Chimeli \& Fisher, 2012), and new scales to measure
maximization have been developed (Diab et al., 2008; Misuraca, Faraci,
Gangemi, Carmeci \& Miceli, 2015; Turner et al., 2012). See Cheek and
Schwartz (2016) for a list and discussion of the existing maximization
scales. Some authors, notably Diab, Gillespie, and Highhouse (2008) and
Giacopelli, Simpson, Dalal, Randolph, and Holland (2013) note that
various measures of maximizing yield different correlations with
indices of well-being, indicating that the scale selection is likely to
influence the results observed in a study. 

Following Rim et al.'s (2011) analyses, Turner et al.  (2012)
developed the 34-item Maximization Inventory (MI). This relatively new
scale has been used by a number of researchers since its publication
(e.g., Djulbegovic et al., 2014; Miller, 2014; Moyano-Díaz et al.,
2014; Patalano, Weizenbaum, Lolli \& Anderson, 2015; Rim, 2017; Rogge,
2016; Sharif \& Spiller, 2014).

MI is the first scale to measure satisficing directly, as a separate
subscale, instead of indirectly through low maximizing scores.
Weinhardt et al.\ (2012) highlight the presence of the Satisficing scale
as an important advancement, as “the data do not support the assumption
that maximizing and satisficing are on opposite ends of a continuum and
therefore developing a satisficing measure is extremely important” (p.
655). Cheek and Schwartz (2016) acknowledge the possible benefits of
measuring satisficing directly, but challenge the content validity and
face validity of MI’s Satisficing subscale. They suggest that, although
the subscale shows internal consistency, some of its items appear to
relate to other constructs than satisficing. Two other subscales of MI
are Decision Difficulty and Alternative Search.

As reported by Turner et al.\ (2012), Decision Difficulty was correlated
with negative indices of well-being, while Alternative Search was
unrelated to them. Meanwhile, Satisficing was associated with adaptive
decision making and good mental health indices (Turner et al., 2012).
Psychometric properties of MI were shown by its authors to be superior
to MS, using both classical test theory and item response analysis.
Weinhardt et al.\ (2012) note the use of general statements in MI as a
significant advantage over MS, which uses specific statements. 

Another maximization scale, the Maximization Tendency Scale (MTS, Diab
et al., 2008), consists mostly of High Standards items. As Weinhardt
et al. (2012) propose, MI is to be perceived as a measure of
maximization behavior, while MTS as a measure of maximization goal
(Cheek \& Schwartz, 2016).

A High Standards subscale, which is a standard component of other
maximization-related scales, is not present in MI. High Standards (HS)
items were present in the original pool of items, and an HS subscale
was considered for MI. However, both exploratory and confirmatory
factor analysis, together with IRT, failed to provide support for High
Standards as a separate factor (Turner et al., 2012). In their recent
review of maximization measures (published after our analysis was
conducted), Cheek and Schwartz (2016) point out that MI does not
contain a High Standards dimension (p.\ 132). However, later in their
review, they argue that “it is not actually having high standards that
defines the goal of maximization” (p.\ 135), as Satisficers can also
have high standards.\footnote{Consider two people who both have high
  standards: one is a maximizer, the other one is a satisficer. The
  maximizer tries to find and evaluate all options available to make
  sure he selects the best one. The satisficer stops the search upon
  finding the first option that meets his (high) standards.} Having
high standards is essential to maximizing, but is not exclusive to it.
Rather than having high standards, Cheek and Schwartz define
maximizing through the desire to choose the best option, the
“maximum”. We acknowledge that MI (and consequently SMI) lacks a
measure of this maximization goal, yet we see MI (especially its
Alternative Search subscale) as a useful measure of behavior relevant
to the goal of maximizing.

Cheek and Schwartz (2016) propose a two-component model of
maximization, distinguishing between maximization goal (choose the
best) and maximization strategy (extensive alternative
search).\footnote{As noted by the editor, there are specific scenarios
  in which an active search is not possible, yet the goal of
  maximization may still be relevant. When selecting from job
  candidates, one usually does not search actively, but simply waits
  for applications to arrive. A maximizer will wait until he is
  reasonably sure that no better candidate will apply. A satisficer
  will accept the first candidate that meets the criteria.} For
maximization goal measurements, they recommend Dalal, Diab, Zhu and
Hwang's (2015) 7-Item Maximization Tendency Scale, as it has good
psychometric properties and focuses on the goal of choosing the
best. For maximization strategy measurements, Cheek and Schwartz
tentatively recommend the use of MI’s Alternative Search subscale.
However, they encourage further refinement of this measure by future
researchers. In this paper, we contribute to such refinement.

Turner et al.\ (2012) report satisfactory psychometric properties of
the overall MI model with three subscales (Cronbach’s alphas ${\geq}$
0.73; RMSEA=0.063). Upon closer inspection, however, some MI items
display low factor loadings. Turner et al.\ (2012) report
$\lambda ${\textless}0.3 for items 5, 7 and 9 of the Satisficing scale
and $\lambda {\leq}$0.4 for 13 out of the total of 34 items). Applying
classical test theory criteria on MI using data reported by Turner et
al.\ (2012) is a challenging task, as some important statistics are
absent (e.g., CFA Chi-squared and CFI/TLI statistics). Item response
theory (IRT) analysis can provide more insight into individual item
performance, and Turner et al.\ (2012) present some IRT analysis
results in their report. The item discrimination parameter for item 24
is 0.59 (according to Baker, 2001, discriminability lower than 0.65 is
considered low). For items 5, 7, 9, 15, 17 and 21, item discrimination
parameters are lower than 0.9. In total, Turner et al.\ (2012) report
item discrimination parameters lower than 1.0 for 12 items of
MI. Items low in this parameter have flatter item information curves
and, relatively to items high in this parameter, contribute poorly to
the total test information. They enhance the total test information
and thus lower errors of latent trait estimates. At the same time,
however, these items also influence (usually increase) the variance of
estimated latent traits and can thus decrease the test
reliability.\footnote{ Test reliability in Item Response Theory is
  usually estimated using the equation r~=~VAR(EAP)/[VAR(EAP) + MSE],
  where VAR(EAP) is the variance of expected a-posteriori latent trait
  estimates and MSE is the mean of error variance of these
  estimates. The resulting reliability thus depends on the mean error
  variance (negatively) and the variance of estimated latent traits
  (positively).} Additionally, Moyano-Díaz et al.\ (2014), who used (a
Spanish translation of) MI in their research, reported poor
performance of the Satisficing subscale. The internal consistency of
the subscale was low (Cronbach’s alpha = 0.64) and the authors
suggested a two-factor solution for this subscale. They also
noted that the meanings of some Satisficing items overlap with
other dimensions of MI.

The three subscales of MI contain a total of 34 items. While a scale
this large is perfectly acceptable for studies in which maximizing is
the focal construct, its rather large size might discourage researchers
from using MI as a supplementary method. When researchers compose a
battery of scales to measure several different constructs, they face a
trade-off between brevity and better psychometric properties. We
believe that one of the reasons for the Maximization Scale’s (Schwartz
et al., 2002) popularity is its conciseness and ease of use. 

Based on these indices, we conjecture that an appropriate shortening of
the Maximization Inventory might produce a scale that is concise,
creates a much smaller burden on participants and provides results
which are as reliable and valid as those from the original scale.
Furthermore, developing a short version of MI is an opportunity to flag
and remove problematic items, should any be identified, resulting in
higher-quality measurement per item.

Turner et al.\ (2012) conducted multiple studies on MI, but all of them
used samples consisting of undergraduate students enrolled in a
psychology course. Such samples differ from the general population in
terms of age distribution, intelligence, and academic achievement.
Moreover, some items may display lower discriminability because of the
lower response variability in a homogenous sample. Examining MI’s
psychometric properties with a different and more heterogeneous sample
is thus desirable. This paper contributes by administering MI to a
diverse sample of subjects (aged 18 to 83, with education levels
ranging from elementary to postgraduate).

In addition, by recruiting subjects from the Czech Republic, this paper
expands maximization research to a new cultural environment. So far,
maximization has been studied in the U.S. (e.g., Rim et al., 2011;
Schwartz et al., 2002; Turner et al., 2012), Italy (Misuraca et al.,
2015), Norway (Lai, 2010), the Netherlands, Belgium, China (Roets,
Schwartz \& Guan, 2012) and Chile (Moyano-Díaz et al., 2014). Roets et
al.\ (2012) found in their cross-cultural study that maximizers in the
U.S. and Western Europe report lower well-being than satisficers. In
China, a collectivist culture with a strong long-term orientation
(Hofstede, 2016) where choice is not as abundant as in the U.S. and
Western Europe, the relationship between maximization and well-being
was insignificant. Compared to the U.S. (Hofstede, 2016), Czech culture
is higher in uncertainty avoidance and long-term orientation and is
lower in individualism. These differences, together with the fact that
the Czech nation faced limited (both consumer and political) choice
opportunities under the communist regime, might be reflected in Czechs’
decision-making and well-being correlates. Following previous research
on maximizing, we use the well-being indices of Happiness (Lyubomirsky
\& Lepper, 1999), Optimism (Scheier, Carver \& Bridges, 1994),
Self-Efficacy (Schwarzer \& Jerusalem, 1995) and Regret (Schwartz et
al., 2002). Although it is not our main motivation, this research
provides the opportunity to investigate whether maximizing has the same
correlates and factor structure in the Czech sample as in the U.S.
sample. The primary focus of the correlation analysis is to provide
evidence for construct validity of the Short Maximization Inventory.

In this paper, we first analyze the Maximization Inventory as
administered to the Czech sample. We replicate the vast majority of
MI’s psychometric properties and well-being indices correlations
reported in Turner et al.\ (2012). We also report more complete
statistics for individual items of MI. We replicate the three-factor
structure proposed in Turner et al.\ (2012); however, using classical
test theory and item response theory, we find multiple items with
sub-standard properties. We proceed to develop a short version of MI,
following the goal of creating a concise scale with solid psychometric
properties. Our main criteria were the overall fit of the model and
exclusion of items that did not substantially contribute towards the
model's good properties. Using a different set of participants, we
then demonstrate the favorable psychometric properties of the new
scale.

By removing poorly performing items and refining both the Alternative
Search and Satisficing subscales, we partially address the suggestions
offered by Cheek and Schwartz (2016) and Weinhardt et al.\ (2012). The
resulting Short Maximization Inventory is a compact yet powerful
measurement tool that might benefit the whole field, as it facilitates
further research on maximizing.

\section{Part 1: Development of the Short Maximization Inventory}
The purpose of this study was to assess the psychometric properties of
the Maximization Inventory (Turner et al., 2012) and to develop a
shortened version of MI. 

\subsection[Method]{Method}
\subsubsection{Scale translation}
With the permission of one of its authors, the Maximization Inventory
was first translated into Czech following guidelines proposed by
Beaton, Bombardier, Guillemin and Ferraz (2000). The process included
three independent translations, back-translations and an expert
committee assessment. As an additional step, two think-aloud cognitive
interviews and two concurrent verbal probing cognitive interviews
(Willis, 1999) were conducted to ensure that the items were clear and
easy to comprehend. Finally, 12 Masaryk University students
participated in the online pilot testing of the translated scale and
reported no difficulties understanding and responding to the items. The
translation and adaptation of the scale into Czech is described in
Ďuriník (2016).

\subsubsection{Participants}
A total of 902 adult individuals participated in this study. Originally,
913 responses were collected. After screening the raw data for
suspicious answer patterns (e.g., 1-2-3-4-5-1-2-3-4-5), too-short
response times (less than one second per item) and invalid responses
(e.g., a reported age of 11,000 years), the responses from 11
participants were removed.

A total of 77 Masaryk University students completed the scale after
being invited to do so via e-mail. 835 members of the general public
were also recruited via \textit{www.vyplnto.cz}, an online platform for
survey participant recruitment. Of the total sample, 29\% were male and
71\% were female. The mean age was 35.4 (SD = 13.62). Each respondent
participated voluntarily, and no reward was promised or given for
participation. 

We randomly assigned approximately two-thirds of the respondents (see
the online supplement for the code) to Data Set 1 (\textit{n}~=~603;
66.9~\%) for exploratory purposes; the rest of the respondents formed
Data Set 2 (\textit{n}~=~299; 33.1\%).

\subsubsection{Procedures}
Participants rated their degree of agreement with 34 items of the
Maximization Inventory on a standard 5-point scale with anchors (1 =
Strongly Disagree; 5 = Strongly Agree). Next, four other scales were
administered (see Part 2 of this paper). With Data Set 1, we assessed
the performance of the 34-item Maximization Inventory and developed the
shortened version. With Data Set 2, we verified the factor structure of
the shortened scale.

\subsubsection{Data Analysis}
All the analyses were carried out using R environment (R Core Team,
2017). We worked under Item Response Theory parametrization – as the
measurement model, we used the confirmatory multidimensional Graded
Response Model fitted using the \textit{mirt} package (Chalmers,
2012).  Model fit was evaluated using M2* statistics (Maydeu-Olivares
\& Joe, 2006) with collapsing over response categories (Cai \& Hansen,
2013).  This allowed us to see if the proposed model (three dimensions
with each item loaded on just one factor) describes the observed data
sufficiently well.\footnote{ The M2* procedure provides asymptotic
  chi-squared statistics of model fit, which can be used directly, or
  to compute \textit{RMSEA} (root mean square error of approximation)
  and interpreted in the same way as in a confirmatory factor
  analysis: \textit{RMSEA} of well-fitting model approaches 0. If the
  M2* statistics are also computed for the null model (in which all
  item discrimination parameters are fixed to 0), incremental fit
  indices such as \textit{CFI} or \textit{TLI} can be computed too and
  values close to 1 (e.g., above 0.90) are usually considered
  good. The last fit statistic we used is \textit{SRMSR} (standardized
  root mean squared residual) which can be interpreted as the squared
  root of the mean difference between model-predicted and observed
  item correlations (similarly to \textit{SRMR} statistic in factor
  analysis). SRMSR approaches zero in a well-fitting model.} We
inspected the standardized residual matrices and \textit{p}-values for
local dependencies using the \textit{LDG}\textit{\textsuperscript{2}}
statistic (Chen \& Thissen, 1997). LDG\textsuperscript{2} is based on
a bivariate table with predicted and observed item response
frequencies. The significant \textit{p}{}-value (e.g., below 0.05)
associated with the \textit{LDG}\textit{\textsuperscript{2}} statistic
suggests a local dependence of two items that is not predicted by the
IRT model. As the \textit{LDG}\textit{\textsuperscript{2}} statistic
is chi-squared distributed, the effect size of residual relations can
be expressed using Cramer’s V as in other chi-squared tests.

The signed chi-squared test (S-X\textsuperscript{2}; Orlando
\& Thissen, 2000), which is also based on the difference between
observed and predicted response frequencies, was used as an item fit
statistic. The significant values of S-X\textsuperscript{2}
suggest that the observed responses to a particular item do not comply
with the IRT model. Reliability was estimated using latent trait
estimates and their associated standard errors; this is the reliability
of latent trait estimated using the IRT model. We also used Cronbach’s
alpha for item sums under classical test theory, as in the original
study (Turner et al., 2012).

\subsection[Results]{Results}
First, we used Data Set 1 to fit the multidimensional graded response
model. The model fitted the data well, M2*~=~1303.5, df~=~422,
\textit{p}~{\textless} 0.001; \textit{RMSEA} = 0.059 with
95\%~\textit{CI}~[0.055, 0.063], \textit{TLI}~= 0.932, \textit{SRMSR}~=
0.083.\footnote{ Note: M2* is the value of chi-squared model fit test
with the appropriate number of degrees of freedom. } Item
discrimination parameters and item fit are shown in Table 1.

Reliability estimates using Cronbach’s alpha were similar to the
original study by Turner et al.\ (2012; reported as
\textit{${\alpha}$}\textit{ original} in Table 1). IRT reliability
estimates were higher for all three subscales, as reported in Table 1.

% table 1
\begin{table*}[t!]\centering
\caption{Maximization Inventory items – results of Item Response Theory
analysis. N=603.}
\begin{tabular}{@{}c@{}C{.8in}ccccccccccccc@{}}\toprule
 & \multirow{2}{.5in}{Survived\newline into SMI} & \mc{3}{c}{Discrimination parameters} &  & \mc{4}{c}{Thresholds} &  & \mc{3}{c}{Item fit} & \\\cmidrule(lr){3-5}\cmidrule(lr){3-5}\cmidrule(lr){7-10}\cmidrule(lr){11-14}
Item No. &  & a\textsubscript{S} & a\textsubscript{DD} & a\textsubscript{AS} &  & d\textsubscript{1} & d\textsubscript{2} & d\textsubscript{3} & d\textsubscript{4} &  & S-X\textsuperscript{2} & df & \itshape p & $\mbox{r}_{xx^\prime}$ $\alpha $ (${\alpha}$ original) \\\midrule
1 & Yes & 1.484 & 0 & 0 &  & 5.40 & 3.28 & 1.39 & $-$1.45 &  & 112.0 & 115 & 0.562 & 0.774 0.711 (0.73)\\
2 & No & 1.204 & 0 & 0 &  & 5.74 & 4.32 & 2.80 & 0.61 &  & 82.5 & 80 & 0.401 & \\
3 & Yes & 1.478 & 0 & 0 &  & 5.06 & 3.47 & 1.20 & $-$1.09 &  & 115.8 & 117 & 0.515 & \\
4 & Yes & 1.547 & 0 & 0 &  & 4.16 & 2.14 & 0.25 & $-$2.45 &  & 135.8 & 143 & 0.653 & \\
5 & No & 1.018 & 0 & 0 &  & 4.84 & 2.78 & 1.32 & $-$0.63 &  & 127.6 & 131 & 0.568 & \\
6 & Yes & 1.372 & 0 & 0 &  & 5.80 & 3.90 & 2.16 & $-$0.35 &  & 106.8 & 97 & 0.233 & \\
7 & No & 0.820 & 0 & 0 &  & 4.32 & 2.48 & 0.84 & $-$0.85 &  & 128.7 & 141 & 0.763 & \\
8 & No & 0.561 & 0 & 0 &  & 4.75 & 3.28 & 2.19 & 0.48 &  & 81.7 & 87 & 0.640 & \\
9 & Yes & 0.824 & 0 & 0 &  & 2.03 & 0.25 & $-$1.17 & $-$2.73 &  & 131.3 & 137 & 0.622 & \\
10 & No & 0.129 & 0 & 0 &  & 4.61 & 2.92 & 1.56 & $-$0.15 &  & 106.8 & 99 & 0.278 & \\\midrule
11 & No & 0 & 2.053 & 0 &  & 1.70 & $-$0.39 & $-$1.71 & $-$3.16 &  & 124.8 & 148 & 0.917 & 0.914 0.891 (0.85)\\
12 & Yes & 0 & 2.722 & 0 &  & 4.00 & 1.22 & $-$0.42 & $-$2.98 &  & 131.3 & 135 & 0.575 & \\
13 & Yes & 0 & 2.477 & 0 &  & 2.69 & 0.73 & $-$0.63 & $-$2.64 &  & 179.2 & 147 & 0.036 & \\
14 & Yes & 0 & 1.868 & 0 &  & 3.08 & 1.48 & 0.14 & $-$1.74 &  & 152.8 & 147 & 0.354 & \\
15 & No & 0 & 1.725 & 0 &  & 1.47 & $-$0.49 & $-$1.90 & $-$3.55 &  & 123.3 & 116 & 0.304 & \\
16 & No & 0 & 1.840 & 0 &  & 1.93 & $-$0.29 & $-$1.74 & $-$3.62 &  & 146.8 & 138 & 0.288 & \\
17 & Yes & 0 & 1.386 & 0 &  & 1.81 & 0.26 & $-$1.22 & $-$2.62 &  & 147.5 & 156 & 0.674 & \\
18 & No & 0 & 1.525 & 0 &  & 2.33 & 0.17 & $-$1.55 & $-$2.80 &  & 138.5 & 148 & 0.700 & \\
19 & No & 0 & 1.609 & 0 &  & 3.63 & 1.62 & 0.28 & $-$1.67 &  & 121.5 & 131 & 0.712 & \\
20 & No & 0 & 1.400 & 0 &  & 2.48 & 0.98 & $-$0.13 & $-$2.02 &  & 156.4 & 155 & 0.453 & \\
21 & No & 0 & 0.477 & 0 &  & 2.88 & 0.98 & $-$0.56 & $-$1.75 &  & 121.2 & 138 & 0.844 & \\
22 & Yes & 0 & 0.956 & 0 &  & 2.73 & 1.18 & $-$0.20 & $-$1.78 &  & 162.2 & 150 & 0.235 & \\\midrule
23 & No & 0 & 0 & 0.758 &  & 3.40 & 1.69 & 0.35 & $-$1.33 &  & 155.5 & 140 & 0.175 & 0.916 0.881 (0.83)\\
24 & Yes & 0 & 0 & 0.899 &  & 1.85 & 0.45 & $-$0.43 & $-$1.84 &  & 179.9 & 168 & 0.251 & \\
25 & No & 0 & 0 & 2.610 &  & 3.45 & 1.17 & $-$0.71 & $-$3.78 &  & 139.0 & 125 & 0.185 & \\
26 & Yes & 0 & 0 & 2.987 &  & 4.43 & 2.11 & 0.07 & $-$3.47 &  & 127.7 & 124 & 0.392 & \\
27 & Yes & 0 & 0 & 2.073 &  & 3.10 & 1.15 & $-$0.46 & $-$2.57 &  & 14.7 & 134 & 0.329 & \\
28 & No & 0 & 0 & 2.249 &  & 3.84 & 1.71 & $-$0.25 & $-$3.07 &  & 157.2 & 129 & 0.046 & \\
29 & Yes & 0 & 0 & 1.974 &  & 2.55 & 0.75 & $-$0.66 & $-$2.96 &  & 13.6 & 138 & 0.661 & \\
30 & No & 0 & 0 & 1.486 &  & 1.29 & $-$0.02 & $-$0.94 & $-$2.47 &  & 162.7 & 153 & 0.280 & \\
31 & No & 0 & 0 & 1.264 &  & 3.91 & 2.14 & 0.46 & $-$1.96 &  & 15.1 & 122 & 0.043 & \\
32 & Yes & 0 & 0 & 1.030 &  & 3.23 & 1.60 & 0.54 & $-$1.22 &  & 98.5 & 124 & 0.955 & \\
33 & No & 0 & 0 & 1.194 &  & 3.79 & 2.28 & 0.54 & $-$1.18 &  & 14.2 & 121 & 0.112 & \\
34 & No & 0 & 0 & 1.184 &  & 2.39 & .89 & $-$0.81 & $-$2.57 &  & 134.6 & 148 & 0.778 & \\\bottomrule
\mc{15}{p{6.2in}}{Note: With factor correlation S–DD
\textit{r} = $-$0.312 $p < .001$, S–AS \textit{r} =
0.119, $p < 0.01$, and DD–AS \textit{r}~= 0.223, $p < .001$.}\\
\mc{15}{p{6.2in}}{$\mbox{r}_{xx^\prime}$ is IRT latent trait estimation
reliability (Kim \& Feldt, 2010).}
\end{tabular}
\end{table*}

Although the model had a good fit, there was a substantial number of
locally dependent items. The \textit{LDG}\textit{\textsuperscript{2}}
test was significant at \textit{p}~{\textless} 0.01 for the 239 item
pairs (43\%), of which 146 pairs (26\%) were more dependent than one
could expect based on the model. This suggests that the responses to
many pairs of items are not driven only by the three measured
dimensions, but to a~small extent also by another hidden factor. This
can be wording, other unmeasured traits, etc. 

Items 2, 6, 8 and 10\footnote{ In this paper, we use Turner et al.’s
  (2012; Table 3) numbering of items. The \textit{Satisficing}
  subscale consists of items 1-10, the \textit{Decision Difficulty}
  subscale consists of items 11-22, and the \textit{Alternative
    Search} subscale consists of items 23-34.} had high skewness,
kurtosis and high mean raw scores (above 4 on a scale ranging 1 to 5),
which led to very high thresholds (especially the d\textsubscript{4}
threshold between responses 4 and 5). All of these items are general
statements about the nature of life and decision making\footnote{ Item
  2: “At some point you need to make a decision about things.”\par \ \
  Item 6: “Good things can happen even when things don’t go right at
  first.”\par \ \ Item 8: “All decisions have pros and cons.”\par \ \
  Item 10: “I accept that life often has uncertainty.”} and do not
refer to specific decision-making situations in life. Judging by their
content, it is easy to understand why most respondents chose extreme
values of 4 or 5 when responding to these items. We flagged these as
potentially problematic; with these items, respondents tend to select
the highest values available, and items thus have low discrimination
ability or low item information.

Items 13, 28 and 31 did not fit an IRT model at \textit{p}~{\textless}
0.05; however, the actual discrepancies were small. Items 7--10 and
21--24 had small discrimination parameters (below 1.0). The
discrimination parameter of item 10 was not significantly different
from 0 (95\% CI~=~[$-$0.055, 0.313]). This means that this item does not
significantly discriminate between people with a higher and lower level
of the satisficing trait.

A residual matrix inspection revealed the tendency of item 10
(\textit{Satisficing} subscale) to have a high residual correlation
with items from the \textit{Decision Difficulty} factor (Cramer’s
V~{\textgreater} 0.12, \textit{Md}~= 0.14), as well as the high
residual correlation of item 5 (\textit{Satisficing} subscale) with
items from the \textit{Alternative Search} factor (Cramer’s
V~{\textgreater} 0.10, \textit{Md}~= 0.14). As the first part of item
5 is essentially a definition of alternative search,\footnote{ Item 5:
  “I try to gain plenty of information before I make a decision, but
  then I go ahead and make it.”} this was not surprising. We also
found high correlated residuals between items 25 and 26 (Cramer’s~V~=
0.26) and between items 23 and 5\footnote{Consider, for example, the
  similarity of item 25 (“I will continue shopping for an item until
  it reaches all of my criteria”) with item 26 (“I usually continue to
  search for an item until it reaches my expectations”).} (Cramer’s
V~= 0.24). These pairs of items are essentially re-wordings of each
other and artificially inflate the measured model fit. Regardless of
the calculated psychometric properties, we consider it redundant to
include two items that ask the same question. Other major inter-item
correlations not explained by the factor were between items 29 and 30
(V~= 0.20), 23 and 31 (V~= 0.19), 16 and 18 (V~= 0.15), 7 and 8 (V~=
0.16), and 15 and 16 (V~= 0.15).

% table 2
\begin{table*}[t!]\centering
\caption{The Short Maximization Inventory model fit statistics.}
\begin{tabular}{lcccccccccc}\toprule
\mc{2}{c}{model invariance} &  &  &  &  &  &  & \mc{3}{c}{model comparison}\\\cmidrule{1-2}\cmidrule{9-11}
 & constrains & $\chi $\textsuperscript{2} & df & RMSEA [95 \% CI] & TLI & BIC &  & $\chi $\textsuperscript{2} & df & \itshape p\\\midrule
configural &  & 154.9 & 84 & 0.031 [0.023, 0.038] & 0.974 & 37330.1 &  &  &  & \\
metric & slopes & 186.9 & 99 & 0.031 [0.024, 0.038] & 0.972 & 37243.0
&  & 14.9 & 15 & 0.456\\
parallel & + intercepts & 244.4 & 159 & 0.024 [0.018, 0.030] & 0.983
& 36898.3 &  & 63.6 & 60 & 0.351\\
\mc{2}{l}{one-group analysis} & 110.2 & 42 & 0.042 [0.033, 0.052] & 0.978 & 36881.1 & ~ & ~ & ~ & \\\bottomrule
\end{tabular}
\end{table*}

% table 3
\begin{table*}[t!]\centering
\caption{Short Maximization Inventory items.}
\begin{tabular}{lll}\toprule
No. & (No. in MI) & Satisficing items \\\midrule
1 & (1) & I usually try to find a couple of good options and then choose
between them.\\
2 & (3) & In life, I try to make the most of whatever path I take.\\
3 & (4) & There are usually several good options in a decision
situation.\\
4 & (6) & Good things can happen even when things don’t go right at
first.\\
5 & (9) & I know that if I make a mistake in a decision that I can go
“back to the drawing board.”\\\midrule
No. & (No. in MI) & Decision Difficulty Items \\\midrule
6 & (12) & I am usually worried about making a wrong decision.\\
7 & (13) & I often wonder why decisions can’t be more easy.\\
8 & (14) & I often put off making a difficult decision until a
deadline.\\
9 & (17) & The hardest part of making a decision is knowing I will have
to leave the item I didn’t choose behind.\\
10 & (22) & I do not agonize over decisions.\\\midrule
No. & (No. in MI) & Alternative Search Items \\\midrule
11 & (24) & I take time to read the whole menu when dining out.\\
12 & (26) & I usually continue to search for an item until it reaches my
expectations.\\
13 & (27) & When shopping, I plan on spending a lot of time looking for
something.\\
14 & (29) & I find myself going to many different stores before finding
the thing I want.\\
15 & (32) & When I see something that I want, I always try to find the
best deal before purchasing it.\\\bottomrule
\end{tabular}
\end{table*}

The results presented in this section provide strong support for our
original conjecture: Maximization Inventory could benefit from having
its poorly performing items removed. The newly developed Short
Maximization Inventory has the potential to display psychometric
properties at least as good as those of the original MI, with the added
benefit of greater conciseness.

We removed the problematic items and kept the best items in terms of
discrimination ability, factor loading, and correlated residuals. Based
on the criteria of very low discrimination ability, we removed items
7--8, 10, 21 and 23. Item 2 was excluded based on its low difficulty and
thus small item information. Other items were excluded based on dual
loadings, sometimes combined with small discrimination parameters.

This led to a final solution with three factors of five items each. This
shortened scale fit the data from Data Set 1 very well, M2*~=~85.6,
df~=~42, \textit{p}~{\textless} 0.001; \textit{RMSEA} = 0.042 with
95\%~\textit{CI}~[0.029, 0.054], \textit{TLI}~= 0.979, \textit{SRMSR}~=
0.047. We cross-validated this model on Data Set 2, where the fit was
excellent as well, M2*~=~69.5, df~=~42, \textit{p}~= 0.005;
\textit{RMSEA} = 0.047 with 95\%~\textit{CI}~[0.026, 0.067],
\textit{TLI}~= 0.971, \textit{SRMSR}~= 0.061.

We then performed a series of multigroup IRT analyses to test scale
invariance. The results in Table 2 indicate that there are no
significant differences between Data Set 1 and Data Set 2. Fixing the
parameters did not enhance the model. Furthermore, the more
constrained model had better fit statistics (BIC\footnote{ Bayesian
  information criteria based on likelihood function, which can be used
  for comparing nested models (differently invariant models are
  nested). Lower value suggests better fitting model. }, TLI, RMSEA)
than the less constrained models. Therefore, we used all the data from
Data Sets 1 and 2 for subsequent analyses. We refer to this scale as
the Short Maximization Inventory (SMI). A list of all 15 items is
presented in Table 3.

All SMI items, except for item 11, have discrimination parameters
greater than 1. The IRT model parameters of the Short Maximization
Inventory are presented in Table 4. Three items (2, 6 and 10) differ
from the Graded Response Model significantly at p~{\textless} 0.05;
however, the total model fit is very good, as one can see in Table 2.
Furthermore, the shortened version of the scale no longer displays
significant correlation between the Alternative Search and Satisficing
subscales. The construct validity is the same as for the full
inventory. Correlations of latent trait estimates for the whole sample
(merged Data Sets 1 and 2) between the Maximization Inventory and Short
Maximization Inventory are quite high (Satisficing \textit{r}~= 0.944,
Decision Difficulty \textit{r}~= 0.937 and Alternative Search
\textit{r}~= 0.950, all \textit{p}~{\textless} 0.001).

We also estimated the reliability for these three scales using IRT
reliability based on latent trait estimates and their associated
errors of estimation, and using conventional Cronbach’s alpha to
assure the comparability with previous research. Furthermore, we also
used Raykov’s omega from ordinal confirmatory factor
analysis,\footnote{ We used the WLSMV estimator (diagonally weighted
  least squares estimator used to estimate model parameters and full
  weighted matrix used to compute robust standard errors) of the
  polychoric correlation matrix in the \textit{lavaan} package
  (Rosseel, 2012). } which provided similar results to the
multidimensional IRT. Raykov’s omegas can be understood as the squared
correlation between the sum of items and the latent trait. Researchers
who wish to use IRT latent trait scores should use
$\mbox{r}_{xx^\prime}$ estimations from Table 4.  Researchers who wish
to work with raw scores (e.g., sums or means of items) should use
Raykov’s omegas ($\omega $ coefficients in Table 4), as Cronbach’s
alphas slightly underestimate the true reliability as they assume
tau-equivalence and the interval scale of items.

% table 4
\begin{table*}[t]\centering
\caption{Short Maximization Inventory parameters of the multidimensional IRT
model: discrimination parameters, thresholds, item fit, and
reliabilities.  N=902.}
\begin{tabular}{lccccccccccccc}\toprule
 & \mc{3}{c}{Discrimination parameters} &  & \mc{4}{c}{Thresholds} &  & \mc{3}{c}{Item fit} & \\\cmidrule{2-4}\cmidrule{6-9}\cmidrule{11-13}
 & a\textsubscript{S} & a\textsubscript{DD} & a\textsubscript{AS} &  & d\textsubscript{1} & d\textsubscript{2} & d\textsubscript{3} & d\textsubscript{4} &  & S-X\textsuperscript{2} & df & \itshape p & Reliability \\\midrule
1 & 1.346 & 0 & 0 &  & 5.28 & 3.18 & 1.25 & $-$1.49 &  & 89.4 & 81 & 0.245 & r\textsubscript{xx}‘~= 0.746 $\omega $~= 0.717 $\alpha $~= 0.695\\
2 & 1.337 & 0 & 0 &  & 5.11 & 3.38 & 1.21 & $-$0.95 &  & 105.1 & 80 & 0.031 & \\
3 & 2.181 & 0 & 0 &  & 5.08 & 2.67 & 0.29 & $-$2.90 &  & 97.1 & 98 & 0.507 & \\
4 & 1.146 & 0 & 0 &  & 5.53 & 3.74 & 2.05 & $-$0.28 &  & 78.0 & 73 & 0.324 & \\
5 & 1.075 & 0 & 0 &  & 2.29 & 0.29 & $-$1.32 & $-$2.97 &  & 117.5 & 108 & 0.251 & \\\midrule
6 & 0 & 2.985 & 0 &  & 4.11 & 1.16 & $-$0.49 & $-$3.16 &  & 123.2 & 94 & 0.023 & r\textsubscript{xx}‘~= 0.855 $\omega $~= 0.794 $\alpha $~= 0.782\\
7 & 0 & 3.067 & 0 &  & 3.22 & 0.87 & $-$0.76 & $-$3.22 &  & 11.0 & 92 & 0.097 & \\
8 & 0 & 1.687 & 0 &  & 2.89 & 1.47 & 0.27 & $-$1.66 &  & 76.9 & 95 & 0.913 & \\
9 & 0 & 1.227 & 0 &  & 1.70 & 0.25 & $-$1.15 & $-$2.56 &  & 106.9 & 105 & 0.429 & \\
10 & 0 & 1.055 & 0 &  & 2.82 & 1.22 & $-$0.12 & $-$1.85 &  & 13.0 & 100 & 0.024 & \\\midrule
11 & 0 & 0 & 0.939 &  & 1.82 & 0.50 & $-$0.37 & $-$1.89 &  & 115.7 & 101 & 0.151 & r\textsubscript{xx}‘~= 0.837 $\omega $~= 0.776 $\alpha $~= 0.773\\
12 & 0 & 0 & 2.489 &  & 4.11 & 1.98 & 0.29 & $-$2.84 &  & 95.2 & 83 & 0.169 & \\
13 & 0 & 0 & 2.871 &  & 3.94 & 1.52 & $-$0.35 & $-$2.98 &  & 101.7 & 81 & 0.060 & \\
14 & 0 & 0 & 2.023 &  & 2.62 & 0.86 & $-$0.63 & $-$2.76 &  & 8.5 & 84 & 0.588 & \\
15 & 0 & 0 & 1.012 &  & 3.27 & 1.67 & 0.60 & $-$1.20 &  & 91.2 & 97 & 0.647 & \\\bottomrule
\mc{14}{p{6in}}{Note: With-factor correlation S-DD
\textit{r} = $-$0.397, $p < .001$ S-AS \textit{r} = 0.059 and
DD-AS \textit{r}~= 0.249, $p < .001$. 
$\mbox{r}_{xx^\prime} - \mbox{IRT}$ latent trait estimation
reliability; $\omega $ --- Raykov’s omega; $\alpha $ – Cronbach’s alpha.}
\end{tabular}
\end{table*}

\section{Part 2: Correlation study }
The purpose of these analyses was to provide evidence about the
construct validity of the Short Maximization Inventory (SMI). We
correlated the SMI scales with measures of constructs that should be,
according to the theory, related to maximization dimensions. We also
correlated the SMI scales with full MI scales to show that the short
scales provide results similar to those of the original scales.

\subsection{Method}
\subsubsection{Measures, Participants, Procedures}
\textbf{Maximization}. The Maximization Inventory (Turner et al., 2012)
consists of three subscales (number of items): Satisficing (10),
Decision Difficulty (12) and Alternative Search (12). The Short
Maximization Inventory, presented in Table 2, consists of three
subscales (number of items): Satisficing (5), Decision Difficulty (5)
and Alternative Search (5). SMI responses were obtained by extracting
responses to respective items of the MI. 

\textbf{Self-Efficacy}. To assess self-efficacy, we used the General
Self-Efficacy Scale (Schwarzer \& Jerusalem, 1995) translated and
validated by Křivohlavý, Schwarzer and Jerusalem (1993). This 10-item
self-reported scale is intended to measure a general sense of perceived
self-efficacy. Responses are indicated on a 4-point scale ranging from
“not true at all” to “exactly true”. Schwarzer and Jerusalem report
Cronbach’s alphas ranging from 0.76 to 0.9 over samples from 23
nations. In our sample, the Cronbach’s alpha was 0.9.

\textbf{Happiness}. To measure subjective happiness, we used the
Subjective Happiness Scale (Lyubomirsky \& Lepper, 1999) in a
translation developed by Kresanová (2015). The scale consists of 4
items, with the fourth item reverse-scored. Responses are obtained on
7-point scales with anchors. Lyubomirsky and Lepper report Cronbach’s
alphas ranging from 0.79 to 0.94 across 14 samples. In our sample, the
Cronbach’s alpha was 0.83.

\textbf{Optimism}. To measure optimism, we used the Life Orientation
Test – Revised (Scheier et al., 1994) as translated by Bek (2007). This
ten-item scale contains four filler items that are not scored and six
scored items, of which three are reverse-scored. Respondents indicated
their responses on a five-point scale ranging from “Strongly agree” to
“Strongly disagree”. Scheier et al.\ report a Cronbach’s alpha of 0.78;
in our sample, Cronbach’s alpha was 0.86.

\textbf{Regret}. To measure regret, we used the Regret Scale (Schwartz
et al., 2002). This scale consists of five items, one of which is
reverse-scored. Participants respond to items on a 7-point scale (1 =
completely disagree, 7 = completely agree). We developed our own
translation of the scale via independent translations,
back-translation, and expert committee discussion. Schwartz et al.
report a Cronbach’s alpha of 0.67; in our sample, it was 0.77.

A total of 902 participants were recruited online. The sample is the
same sample used in Study 1. After taking the Maximization Inventory,
participants were administered the Life Orientation Test --- Revised,
General Self-Efficacy Scale, Subjective Happiness Scale and Regret
Scale.

\subsubsection{Data analysis}
First, we analyzed raw scores, defined as the sums of items. Then, we
performed ordinal confirmatory factor analysis (CFA).\footnote{ CFA
  was performed in the \textit{lavaan} package (Rosseel, 2012) with
  WLSMV estimation based on polychoric correlation matrices.} We
performed unidimensional CFA for each scale of the Maximization
Inventory to check the structure of each scale. Then we performed a
multidimensional CFA for all these scales and for the full and the
shortened version of MI. Reliabilities were estimated using Revelle’s
omega. This measure outperforms Cronbach’s alpha as it does not assume
tau-equivalent items (the same factor loadings for all items).

We used ordinary fit statistics with common cut-values. 

\subsection{Results}
\subsubsection{Raw scores}
We investigated the relationship of the Short Maximization Inventory’s
subscales to the original full-length subscales as well as to other
measures. To do so, we summed responses for each (sub)scale for each
participant and then used Pearson correlations to assess the
relationship intensity. The descriptive statistics are reported in
Table 5.

% table 5
\begin{table}[t]\centering
\caption{Descriptive statistics for scales used in Study 2.}
\begin{tabular}{lccccc}\toprule
 & N & Min & Max & Mean & S.D.\\\midrule
SMI-Satisficing & 902 & 5 & 25 & 18.35 & 3.216\\
SMI-Decision difficulty & 902 & 5 & 25 & 15.53 & 4.732\\
SMI-Alternative search & 902 & 5 & 25 & 16.30 & 4.620\\
Happiness & 902 & 4 & 28 & 18.60 & 5.138\\
Optimism & 902 & 6 & 30 & 20.30 & 5.409\\
Self-Efficacy & 902 & 10 & 40 & 29.10 & 5.768\\
Regret & 902 & 5 & 36 & 18.11 & 6.588\\\bottomrule
\end{tabular}
\end{table}

First, we examined the correlations of the original Maximization Scale
subscale to their corresponding shortened versions. In all three cases,
the correlations are strong: Satisficing (\textit{r} = 0.87, \textit{p}
{\textless} 0.01), Decision Difficulty (\textit{r} = 0.93,\textit{ p}
{\textless} 0.01) and Alternative Search (\textit{r} = 0.94, \textit{p}
{\textless} 0.01). This indicates that the shortened MI scales measure
the same constructs as the full scales. 

The \textbf{Satisficing }scale of SMI was positively correlated with the
indices of well-being: happiness (r = 0.53, \textit{p} {\textless}
0.01), optimism (\textit{r} = 0.56, \textit{p} {\textless} 0.01) and
self-efficacy (\textit{r} = 0.61, \textit{p} {\textless} 0.01). These
findings are in line with the relationships reported by Turner et al.
(2012), as well as with Schwartz's (2007) and Schwartz
et al.'s (2002) proposed relation of satisficing to
individual well-being. Additionally, satisficing was moderately
negatively related to regret (\textit{r} = $-$0.26, \textit{p}
{\textless} 0.01).

The \textbf{Decision Difficulty} scale was negatively related to all
three well-being indices: happiness (\textit{r} = $-$0.45, \textit{p}
{\textless} 0.01), optimism (\textit{r} = $-$0.44, \textit{p} {\textless}
0.01) and self-efficacy (\textit{r} = $-$0.51, \textit{p} {\textless}
0.01). Decision difficulty was positively related to regret (\textit{r}
= 0.57, \textit{p} {\textless} 0.01). Turner et al.\ (2012) and Rim et
al. (2011) report no significant relationship between decision
difficulty and happiness. This inconsistency cannot be explained by the
shortening of the scale (as the full-sized Decision Difficulty subscale
administered to our sample was also negatively correlated with
happiness, \textit{r} = $-$0.44, \textit{p} {\textless} 0.01). We argue
that the different correlations are related to the nature of the
samples used (U.S. vs.\ Czech sample). This argument is further developed
in the discussion part of this paper.

We found the \textbf{Alternative Search} scale of SMI to be weakly
negatively related to happiness (\textit{r} = $-$0.11, \textit{p}
{\textless} 0.01) and optimism (\textit{r} = $-$0.14, \textit{p}
{\textless} 0.01), unrelated to self-efficacy (\textit{r} = 0.03,
\textit{p} {\textgreater} 0.05) and weakly positively related to regret
(\textit{r} = 0.21, \textit{p} {\textless} 0.01).

Table 6 provides correlations of SMI scales with each other, as well
as with well-being measures. The correlations for the full-sized
34-item MI we administered are provided in brackets. It is evident
that the shortened scale correlates with measures of well-being
similarly to the full scale. The correlations found are similar to
those reported by Turner et al.\ (2012), with the exception of the
relationship between Decision Difficulty and Happiness, mentioned
above. We did not compare the correlations with the Regret scale, as
Turner et al.\ (2012) used the Decision-Making Style Inventory (Nygren
\& White, 2002) for regret assessment, whereas we used the Regret
Scale (Schwartz et al., 2002).

% table 6
\begin{table*}[t]\centering
\caption{Correlations of SMI and MI with measures of well-being. }
\begin{tabular}{ld{2.6}d{2.6}@{\qquad}d{2.6}d{2.6}@{\qquad}d{2.6}d{2.6}}\toprule
 & \mc{2}{c}{SMI-S (MI-S)} & \mc{2}{c}{SMI-DD (MI-DD)} & \mc{2}{c}{SMI-AS (MI-AS)}\\\midrule
SMI-S & 1 & (0.873) & -0.342 & (-0.328) & 0.044 & (0.078)\\
SMI-DD & -0.342 & (-0.220) & 1 & (0.928) & 0.196 & (0.196)\\
SMI-AS & 0.044 & (0.066) & 0.193 & (0.234) & 1 & (0.944)\\
SHS & 0.529 & (0.406) & -0.454 & (-0.440) & -0.111 & (-0.100)\\
LOT-R & 0.556 & (0.398) & -0.443 & (-0.448) & -0.138 & (-0.133)\\
GSES & 0.612 & (0.514) & -0.510 & (-0.495) & -0.030 & (0.008)\\
Regret & -0.262 & (-0.202)  & 0.571 & (0.618) & 0.221 & (0.194)\\\bottomrule
\end{tabular}
\end{table*}

\subsubsection{Construct validity (latent traits)}
The model fit for Maximization Inventory was presented in Study 1 (there
we presented the result of the IRT model, the fit of the ordinal CFA
was similar). For all the other scales, the model fit the data well. 

\textbf{SHS:} $\chi $\textsuperscript{2}(2) = 20.97, \textit{p}
{\textless} 0.001, TLI = 0.987, RMSEA = 0.103 with 95\% CI [0.066;
0.144], SRMR = 0.015. Although the RMSEA is very high, for CFAs with
small degrees of freedom it is not a reliable indicator of fit (Kenny,
Kaniskan \& McCoach, 2015). Reliability was good, $\omega $~= 0.832.

\textbf{LOT-R:} $\chi $\textsuperscript{2}(9) = 255.41, \textit{p}
{\textless} 0.001, TLI = 0.944, RMSEA = 0.174 (95\% CI = [0.156;
0.193]), SRMR = 0.054. The same RMSEA issue holds here as holds for
SHS; reliability was good, $\omega $~= 0.872.

\textbf{GSES:} $\chi $\textsuperscript{2}(35) = 513.55, \textit{p}
{\textless} 0.001, TLI = 0.939, RMSEA = 0.123 (95\% CI = [0.114;
0.133]), SRMR = 0.055 with good reliability $\omega $~= 0.901

\textbf{Regret:} $\chi $\textsuperscript{2}(5) = 247.7, \textit{p}
{\textless} 0.001, TLI = 0.854, RMSEA = 0.232 (95\% CI = [0.208;
0.257]), SRMR = 0.068. Because the fit was not good, we inspected the
residual correlation matrix and discovered a high residual correlation
between items 4 and 5 (\textit{r}~= 0.159). We therefore allowed for
residual covariances between these items, which improved the fit,
$\Delta \chi $\textsuperscript{2}(1)~=~115.9, \textit{p~}{\textless}
0.001. The final model fit the data very well (except RMSEA; see
above), $\chi $\textsuperscript{2}(4) = 67.84, \textit{p} {\textless}
0.001, TLI = 0.952, RMSEA = 0.133 (95\% CI = [0.106; 0.162]), SRMR =
0.034. Reliability was acceptable,\footnote{ Note that Revelle’s omega
  accounts properly for residual correlations, which therefore do not
  bias the reliability estimate.} $\omega $~= 0.732.

For both MI and SMI, the correlations with latent traits (Table 7) are
quite high.  We performed two CFAs over all the scales for both
versions of MI. The fit of the full model with the Short Maximization
Inventory was acceptable, $\chi $\textsuperscript{2}(718) = 3153.27,
\textit{p} {\textless} 0.001, TLI = 0.915, RMSEA = 0.061 (95\% CI =
[0.059; 0.064]), SRMR = 0.058. The fit with the full Maximization
Inventory was poorer, $\chi $\textsuperscript{2}(1630) = 6526.63,
\textit{p} {\textless} 0.001, TLI = 0.883, RMSEA = 0.058 (95\% CI =
[0.056; 0.059]), SRMR = 0.072; the TLI was particularly low.

% should we say more about Table 7?

% table 7
\begin{table*}[t]\centering
\caption{Construct validity for
Maximization Inventory and Short Maximization Inventory. Correlations
of latent traits. N~=~902.}
\begin{tabular}{l*{7}{d{2.6}}}\toprule
 & \mc{1}{c}{MI-S} & \mc{1}{c}{MI-DD} & \mc{1}{c}{MI-AS} & \mc{1}{c}{SHS} & \mc{1}{c}{LOT-R} & \mc{1}{c}{GSES} & \mc{1}{c}{Regret}\\\midrule
MI-S & 1 & -0.402 & 0.129 & 0.648 & 0.677 & 0.759 & -0.332\\
MI-DD & -0.428 & 1 & 0.254 & -0.497 & -0.504 & -0.568 & 0.715\\
MI-AS & 0.071 & 0.257 & 1 & -0.117 & -0.145 & -0.004 & 0.214\\
SHS & 0.692 & -0.549 & -0.146 & 1 & 0.787 & 0.623 & -0.434\\
LOT-R & 0.722 & -0.541 & -0.168 & 0.787 & 1 & 0.599 & -0.461\\
GSES & 0.780 & -0.595 & -0.057 & 0.623 & 0.600 & 1 & -0.430\\
Regret & -0.330 & 0.702 & 0.256 & -0.433 & -0.460 & -0.428 & 1\\\bottomrule
\mc{8}{p{5in}}{Correlations above $\pm .145$ are
significant on $\alpha = .001$ and all correlations above .117 are significant on
$\alpha = .01$}\\
\mc{8}{p{5in}}{Below the diagonal are the results for the model with the Short
Maximization Inventory, above the diagonal are the results for the
original Maximization Inventory.}
\end{tabular}
\end{table*}

\subsection{Conclusions}
Strong correlations between the original subscales and their short
versions indicate that the Short Maximization Inventory is a compact
measurement tool that is equivalent to the original Maximization
Inventory. Concerning correlations with well-being indices, the results
we found for SMI are similar to what we, in line with Turner et al.
(2012), found for the full MI: decision difficulty and alternative
search are negatively related to the indices of well-being and
positively related to regret. Satisficing is positively related to the
indices of well-being and negatively related to regret, suggesting that
satisficing is related to positive adaptation. The validity of SMI is
thus supported by two pillars: the correlations found for SMI are in
line with our theoretical predictions, and they replicate the
correlations found for the full MI.

\section[General Discussion]{General Discussion}
In this paper we pointed out several problems with the original
Maximization Inventory (Turner et al., 2012). Eliminating problematic
items from the MI, we developed a 15-item Short Maximization Inventory
(SMI). This newly developed SMI performs well in measuring individual
dimensions related to maximization. It also displays psychometric
properties that are comparable or better than those of the original MI.
Finally, thanks to its brevity, SMI is less taxing on respondents.

After administering the MI to 902 participants, we found that several of
its items display a ceiling effect. These items were mostly general
statements that are easy to relate to and agree with (e.g., MI item 8:
“All decisions have pros and cons”). Items with heavily skewed
responses have low discriminatory power, as most subjects selected
“Strongly Agree”. 

Highly correlated residuals indicated item overlap. Overlapping items
are, in effect, merely paraphrases of each other, and their presence
does not improve scale performance. We found and excluded several such
cases (e.g., item 25, “I will continue shopping for an item until it
reaches all of my criteria,” and item 26, “I usually continue to search
for an item until it reaches my expectations”).

Some items of the MI tend to load onto more than one factor (e.g., item
5: “I try to gain plenty of information before I make a decision, but
then I go ahead and make it” is connected with both Satisficing and
Alternative Search). We developed the Short Maximization Inventory by
excluding problematic items from the original MI while retaining the
items with satisfactory item discrimination, high factor loading, and
low correlated residuals. SMI consists of three subscales of five items
each.

In general, a scale with more items allows for finer discrimination
among respondents and potentially captures very high and very low
levels of trait better. On the other hand, presenting subjects with
long questionnaires may result in fewer responses and lower response
quality (Galesic \& Bosnjak, 2009). Therefore, MI’s size (34 items)
might be discouraging for researchers who intend to use it as a
supplementary method in their research alongside other scales. In
developing Short Maximization Inventory, we removed from MI the items
with the lowest discrimination and with the lowest factor loadings.
This minimizes the loss of favorable properties associated with scale
shortenings. Furthermore, our analysis shows that SMI measures the same
construct as MI and discriminates between respondents well. SMI allows
researchers to use a measure of maximization that has good psychometric
properties yet is compact and convenient to administer.

The Short Maximization Inventory model showed a good fit with the data
we used to develop it, as well as with an independent sample of
subjects. The scales of SMI correlate very strongly with the scales of
the full MI, indicating they are measures of the same constructs.

Turner et al.\ (2012) provided evidence for the construct validity of
MI’s three scales by correlating them with measures of well-being:
happiness, optimism, and self-efficacy. With SMI, we found the same
relationships between maximization dimensions and well-being that
Turner et al.\ (2012) found with the full MI. The only exception was
that we found a significant negative correlation between Decision
Difficulty and happiness, while Turner et al.\ (2012) reported no
significant relationship. However, this difference cannot be attributed
to the scale reduction as, in our sample, the full 12-item Decision
Difficulty scale also correlated negatively with happiness. The
difference between our result and Turner et al.’s (2012) may be caused
by cultural differences between the U.S. sample used in the earlier
study and the Czech sample we used. According to Hofstede (2016),
Czechs are significantly higher than Americans in uncertainty
avoidance. High uncertainty avoidance corresponds to more negative
feelings related to uncertainty and ambiguity. Therefore, Czech people
who perceive their decisions to be difficult are likely to experience
more negative feelings and lower happiness levels than Americans. 

Based on Parker, Bruine de Bruin and Fischhoff (2007); Rim et al.
(2011); Schwartz et al.\ (2002); and Turner et al.\ (2012), we expected
high Satisficing scores to be associated with the positive indices of
well-being, and high Decision Difficulty and Alternative Search scores
to be associated with the negative indices of well-being. Our
correlation analysis provides evidence for SMI’s construct validity:
Satisficing displays significant positive correlations with the indices
of well-being, while Alternative Search and Decision Difficulty show
negative correlations with well-being. In line with Schwartz et al.’s
(2002) reasoning, we find regret to be negatively related to
Satisficing and positively related to Alternative Search and Decision
Difficulty. That said, we do not consider SMI’s (or MI’s) Satisficing
subscale to be perfect, as we reflect in the \textit{Limitations}
section of the discussion. 

As reviewed by Cheek and Schwartz (2016), there are 11
maximization-related scales available at this time. The reason we have
chosen to introduce yet another one is that we recognize the
Maximization Inventory’s (Turner et al., 2012) solid psychometric
properties relative to other scales, and our short version further
improves on this quality. The Short Maximization Inventory displays
excellent properties, as judged from both the Classical Test Theory and
Item Response Theory viewpoint. Although Cheek and Schwartz (2016)
offer some criticism of the Maximization Inventory, they tentatively
recommend the use of its Alternative Search subscale in research.
Moreover, they encourage researchers to further refine the measurement,
which we have done by formulating SMI. 

\subsection{Limitations of the study}
The primary purpose of the Confirmatory Factor Analysis is the
confirmation of an already existing model, not the development of a new
one. Although our use of CFA in shortening the scale can be identified
as a limitation of the study, our intention was not to develop a new
model but to simplify one that already existed. We thus adopted an
approach similar to that used by Nenkov et al.\ (2008), who shortened
the original Maximization Scale. Once the short scale was developed, we
used CFA again with an independent data set to verify our new model in
a pure, confirmation-only setting.

SMI, just like the original Maximization Inventory, does not contain a
High Standards subscale. Although items relating to having high
standards were originally considered when developing MI, Turner et
al.\ (2012) did not include these items. Subsequently, a measure of
high standards or the desire to choose the best is absent from SMI
too.  Cheek and Schwartz (2016), however, present strong arguments
that the goal of choosing the best, together with the strategy of
alternative search, is an essential component of maximizing. We
recognize this and, following Cheek and Schwartz (2016), recommend
using the 7-Item Maximizing Tendency Scale (MTS-7) developed by Dalal
et al.\ (2015) to measure the maximizing goal of choosing the
best. The MTS-7 together with SMI may provide a complex measurement of
the maximization construct. However, future research should focus on
the incremental validity of MTS-7 over SMI (or MI) subscales and on
the existence of the single high standards factor within the
maximization model.

A novel feature of MI (and consequently SMI) is the presence of the
Satisficing subscale. Turner et al.\ (2012) argue that satisficing is
not simply the lack of maximizing, but an adaptive trait of its own.
Although the Satisficing subscale of both MI and SMI shows good
psychometric properties, concerns have been raised about its content
validity (Cheek \& Schwartz, 2016), incremental validity (Moyano-Díaz
et al., 2014) and reliability (Dewberry, Juanchich \& Narendran,
2013). We acknowledge these concerns. Some of the Satisficing subscale
items are difficult to interpret. Consider for example item 1
\textit{“I usually try to find a couple of good options and then
  choose between them”. }Agreement with this item signifies
satisficing, but what does disagreeing with this item mean? Maybe the
respondent considers many options in an effort to pick the best one,
or maybe he accepts the first alternative he comes across. The
Satisficing subscale of MI (and SMI) is internally consistent and
correlates with the indices of well-being as predicted by the
theory. On the other hand, its face validity is dubious (Cheek and
Schwartz, 2016, relate some of its items to uncertainty tolerance and
to “make the best of the situation” approach, rather than to
satisficing). That said, satisficing conceptualized as a construct
distinct from maximizing may be worth studying in the future, if the
concept of satisficing as anything other than ``not maximizing'' can
itself be clarified.

SMI was not administered to participants as a separate scale. Instead,
we administered the full MI and then extracted the items that compose
SMI. This approach is identical to that of Nenkov et
al.'s (2008) Analysis 3. Although this is not likely,
item responses may have been influenced by the context of other items
presented (Knowles \& Condon, 2000). Related to this issue, Smith,
McCarthy and Anderson (2000) note that this approach is likely to result in
overestimated correlations between the short form and the full form of
the scale. We acknowledge this, but we still consider our results
valid; we not only report high correlations between the full MI and SMI
but also find correlations with the indices of well-being similar to
those reported by Turner et al.\ (2012) for a different dataset.
Following this, a suggested direction for future research is to conduct
a study using the Short Maximization Inventory as a separate scale.

Examining the test-retest validity of SMI would provide useful
information on the stability of results obtained with this scale over
time. We also encourage researchers to contrast SMI results with
behavioral measures associated with maximizing and satisficing to shed
more light on the topic. 

Data for our convergent validity investigation were collected from all
subjects, for all constructs, using the same scales. This poses the
risk of inflated correlations due to common-method bias (Podsakoff,
MacKenzie, Lee \& Podsakoff, 2003). On the other hand, a similar
approach was used for assessing the convergent validity of the original
MI (Turner et al., 2012), and the authors reported no issues related to
common-method bias. Our aim was to demonstrate that the SMI produces
correlations to the indices of well-being similar to those of other
scales. We did not want to research in depth the relationship between
maximization and other constructs.

Administering the scales in Czech translation poses the threat of shifts
in the meanings the items convey. We exercised great care to mitigate
this risk by following (and exceeding) Beaton et al.'s
(2000) guidelines on cross-cultural adaptation of scales. We obtained
three independent translations and back-translations of the items,
commissioned an expert committee to assess the translations and to
select the most appropriate ones. We also conducted two types of
cognitive interviews and pilot-tested the translated scales. Compared
to other studies using non-English measures of maximizing, we dedicated
more effort to ensuring that the translation was correct with no loss
or distortion of meaning of the items (compare, e.g., with Roets et
al., 2012, who had one person translate the scale and “double-checked
the final translation with other colleagues” or Lai, 2010, who used
only iterated translation and back-translation). Our correlation study
results, similar to those reported by Turner et al.\ (2012), indicate
that the translation process was successful and that our study does not
suffer from significant cultural differences.

The aim of this paper was to verify the psychometric properties of MI
and to provide researchers with its shorter yet well-performing
version. We believe this has been accomplished. We consider the results
to be robust, given our sample size of 902 (comparable to N=828 in
Turner et al., 2012). To achieve a balance between our model’s fit with
the data and its predictive power, we split responses randomly into two
data sets. We demonstrate very good fit with both data sets. 

The main contribution this paper reports on is the development of the
Short Maximization Inventory (SMI). SMI contains 15 (5+5+5)
best-performing items of the Maximization Inventory (Turner et al.,
2012), which has 34 (10+12+12) items. As demonstrated in this paper,
SMI is an effective yet concise tool for assessing maximization as an
individual trait. We expect it, or at least its subscales for Decision
Difficulty and Alternative Search (given the need for further
conceptual clarification of satisficing itself) will be well received
by researchers who wish to investigate maximization as a supplementary
measure in their research projects. This compact yet powerful tool for
maximization measurement will allow researchers to expand their
research scope without dramatically inflating the number of items
presented to subjects. To measure the two-component construct of
maximization, as it is presented by Cheek and Schwartz (2016), the
Alternative Search subscale of SMI together with MTS-7 (Dalal et al.,
2015) appears the most appropriate.

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