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PROCEEDINGS OF THE SEVENTEENTH
INTERNATIONAL CONFERENCE ON INFORMATION SYSTEMS
December 16-18, 1996 Cleveland, Ohio
Editors
Janice I. DeGross Sirkka Jarvenpaa Ananth Srinivasan
University of Minnesota University of Texas, Austin University of Auckland
In association with
Special Interest Group on Management College on Information Systems
Information Systems, INFORMS
Association for Computing Machinery
Association for Information Systems The Society for Information
Management
Technical Committee 8: Information Systems, International Association for
International Federation for Information Processing Information Management
Clic
21
A PARTIAL LEAST SQUARES LATENT VARIABLE MODELING
APPROACH FOR MEASURING INTERACTION EFFECTS:
RESULTS FROM A MONTE CARLO SIMULATION STUDY
AND VOICE MAIL EMOTION/ADOPTION STUDY
Wynne W. Chin
Barbara L. Marcolin
Peter R. Newsted
University of Calgary
Abstract
The ability to detect and accurately estimate the strength of interaction effects are critical issues that are
fundamental to social science research in general and IS research in particular. Within the IS discipline, a
large percentage of research has been devoted to examining the conditions and contexts under which
relationships may vary, often under the general umbrella of contingency theory ( McKeen, Guimaraes, and
Wetherbe 1994; Weill and Olson 1989). In our survey of such studies where such moderating variables are
explored, a majority fail to either detect and/or provide an estimate of the effect size. In cases where effects
sizes are estimated, the numbers are generally small. These results have, in turn, led some to question the
usefulness of contingency theory and the need to detect interaction effects (e.g., Weill and Olson 1989). This
paper addresses this issue by providing a new latent variable modeling approach that can give more accurate
estimates of such interaction effects by accounting for the measurement error in measures which attenuates
the estimated relationships. The feasibility of this approach at recovering the true effects is demonstrated
in two studies: a simulated data set where the underlying true effects are known and a Voice Mail adoption
data set where the emotion of enjoyment is shown to have both a substantial direct and interaction effect on
adoption intention.
1. INTRODUCTION
The goal of assessing the interaction effects between quantitative (i.e., continuous) variables represents a long tradition in IS
research. Both empirical and theoretical models can easily be found going back several decades (e.g., Powers and Dickson
1973; Ginzberg 1979; Franz 1979). Yet, the ability to detect and accurately estimate such effects can be difficult. Recent
articles bemoan the statistical difficulties inherent in the analysis of interactions in field research and observational studies (e.g.,
McClelland and Judd 1993). These problems include those resulting from measurement error and the low statistical power that
can result from such error. In particular, under conditions of measurement error, traditional techniques such as analysis of
variance (ANOVA) or moderated multiple regression (MMR) may not be able to detect such interaction effects. When
detected, again due to measurement error, the estimate of the true effect may be biased downwards.
In general terms, an interaction effect involves a moderator variable which can be qualitative (e.g., gender, race, class) or
quantitative (e.g., age, income). The moderator, in turn, affects the direction and/or strength of the relation between an
independent or predictor variable and a dependent or criterion variable. Thus, moderator variables provide information as to
the conditions in a which we would expect a relationship between two variables to exist.
Acknowledgments: This research was supported in part by a grant from the Social Sciences and Humanities Research
Council of Canada, whose assistance is gratefully acknowledged. We also wish to thank Theodora Lo for her assistance in the
literature review and simulation runs.
Chin, Marcolin and Newsted
22
Consider the following example. Suppose we are studying the relationship depicted in the Technology Acceptance model
(Davis 1989) which states that the stronger a person’s belief in the usefulness of an IT for enhancing their job performance,
the more they would intend to use it. Yet we also believe that the impact of this perception on IT usage intention is negatively
moderated by the level of enjoyment the individual has during his or her use of the IT. In essence, when the usage experience
is more enjoyable, the impact of perceived usefulness (at whatever level) on future intention to use is lower. Conversely, the
less enjoyable one perceives the IT to be, the stronger the impact of one’s perception of usefulness on intention to use. This
phenomenon is based on a cognitive consistency argument where the underlying rule is that when IT usage is extremely
enjoyable, instrumental issues such as perceived usefulness ought not to come into one’s decision making criteria for future
usage. Thus, all else being equal, if we had two different groups of people where the first group perceived the IT to be highly
enjoyable and the second group the opposite, we would expect a low to possibly negative correlation between perceived
usefulness and IT adoption intention for the first group and a high correlation for the second group. In this scenario, the
dependent variable (Y) would be IT usage intention with the predictor (X) and moderator (Z) variables being perceived
usefulness and enjoyment respectively.
Ideally, we would like to be able to detect such an interaction effect easily (should it exist) and more importantly provide an
accurate estimate of the effect size of the interaction. The traditional approach for detection has been ANOVA, which generally
provides an ability to detect the existence of an interaction effect. Yet, the effect size of an interaction as measured by
additional variance explained is normally not provided and must be explicitly calculated from the sum of squares information.
Alternatively, the use of MMR allows one to both detect and examine two estimates of the interaction effect. The first,
identical to ANOVA, is the additional variance explained. This is assessed by the increase in R-square when the interaction
term (i.e., X*Z) is included in a regression model with the main effects (i.e., X and Z). This is determined by subtracting the
R-square for the two variable main effects model (Y regressed on X and Z) from the R-square for the three variable interaction
model (Y regressed on X, Z, and X*Z). In addition to the change in R-square, the estimated beta for the interaction term
provides additional information regarding the interaction effect. This estimate informs us as to how much a unit change in the
moderator variable Z would change the regression relationship of Y on X.
Yet, both approaches assume that the measures used to predict the dependent variable are without error. In general, social
science data are more than likely measured with error. This bias, in turn, can have substantial impact on the conclusions that
IS researchers may make. For example, if the reliability of the predictor (X) and moderator (Z) variables is 0.70 and their
correlation is 0, then the reliability of the product term (X*Z) representing the interaction effect would be 0.49. The
implication is that, in the best of all situations, an estimate of the proportion of the dependent variable (Y) explained by the
interaction term will be half of the true effect. In other words, suppose the real interaction effect has a R-square of 0.30. Yet,
due to the measurement error, a researcher using MMR would end up with an estimate of 0.15! Furthermore, in addition to
providing downward biased estimates, such unreliable measures will also result in a reduction in the statistical power to detect
such effects.
Therefore, this paper addresses several issues and questions. The first primary question concerns the extent to which previous
IS contingency research applied analytical techniques which assume infallible measures (i.e., ANOVA and multiple regression).
In turn, what proportion of these studies were actually successful in detecting and estimating the interaction effect? If the
majority of the studies suggest weak or negligible effects, can a meta-analytic type of conclusion be made questioning the value
of such interaction studies and contingency theory in general? Alternatively, are the past results and conclusions possibly a
byproduct of the analysis technique? A second primary concern addressed in this paper is to present a new latent variable
modeling approach for better estimation and detection of the interaction effect between quantitative (i.e., continuous) predictor
and moderator variables. To the best of our knowledge, the use of product indicators in a Partial Least Squares (PLS) analysis
to model interaction effects has never been done. The performance ability of this approach is tested on simulated data where
the underlying population parameters (i.e., true effects) are known. Finally, it is further tested on actual data, where the
interaction effect size detected is stronger than those typically found in IS research.
2. LITERATURE REVIEW
Moderators have been used in the IS field for some time and are couched under terms such as multiplicative terms, moderators,
contingency terms (sometimes under contingency theory), and interaction effects.
A Partial Least Squares Latent Variable Modeling Approach
All articles in MIS Quarterly, Information Systems Research, Management Science, Journal of MIS, Decision Sciences,
1
Communications of the ACM, Information & Management and proceedings of ICIS and HICSS up to 1995 and as far back as
the journal goes or 1980, whichever is more recent.
23
In our review of information systems literature back to 1980, moderators were found to be present from the start. In 1980,
1
Schonberger considered how information systems design approaches lead to good systems but only when the contingent factors
are appropriately matched (i.e., information needs for MIS supporting functions and type of decision making). Recently, in
1994, McKeen, Guimaraes and Wetherbe summarized the contingency studies which existed on the relationship between user
participation and satisfaction and found that two out of four moderating variables, task and system complexity, changed the
outcome. However, these two moderators only had a small effect on satisfaction (beta=.03). The authors then concluded that
these moderating variables were probably not the only two important ones and suggested five other promising moderators for
future investigation. From their experience, the unmoderated relationship was not adequate for an investigation into user
participation and satisfaction. Throughout the years, similar studies employing moderators can be found in information systems
research.
Of the 8,110 potential articles over the fifteen year period for the journals we reviewed, seventy articles contained moderator
variables (see Tables 1 and 2). Seven of the articles containing moderators had actually calculated path estimates, with the
remaining sixty-three articles lacking sufficient information or analysis techniques to facilitate an estimate of the moderator
effect size. Thus, while moderators are being examined in the information systems field, the dearth of detailed information may
be a major reason for the slow progress and lack of cumulative knowledge. For instance, only three articles had standardized
coefficients to enable comparison while the other articles published unstandardized coefficients without standard deviations
(from which they could be standardized), split the sample, or failed to report the effect size.
Overall, moderating variables in IS studies tend to be evaluated in a quantitative sense, typically using categorical or interval
scale variables. The majority of articles applied an analysis of variance technique for variables measured with categorical
scales, while a small sub-group applied a regression/path analysis based technique for variables measured with interval Likert-
type scales.
Of the articles identified with moderators (n=70), ANOVA was the predominate technique used for the analyses (51.4%
including ANCOVA), with MANOVAs (14.3% including MANCOVA), multiple regression (10% including path analysis),
and various sundry other analytic techniques (24.3% including theoretical moderators and meta-analyses) following in
popularity.
The studies using analysis of variance approaches (i.e., ANOVA, MANOVA, MANCOVA, ANCOVA), however, did not
provide an estimate of the effect size between the independent and dependent variables but only an indication that the
relationship is significant or not. From these analyses it is not possible to determine the effect size for the significant results.
The degree to which the phenomena exists in the population remains a mystery for 65.7% of the studies reviewed (see Table 1).
A total of 321 moderators were investigated in the articles with 65 assessed as significant, but the majority of these (53) did
not report effect size estimates.
Moreover, the regression and path analysis techniques, which do provide beta path coefficients, had few significant terms, small
effect sizes and low power (see Table 2). Twelve of twenty-two moderating variables were found to be significant in these
articles. The literature consistently reported moderators with a small effect size, beta averaging 0.10, suggesting that the
moderating terms play only a small part for understanding information systems issues. Such a low number of significant
moderators, overall, does not bode well for the impact these lines of investigation have had on the IS field. These moderating
terms do not seem to be good contributors to the body of knowledge.
Statistical power also is rarely discussed in these studies. Given that power is a factor in assessing the ability of the tests to
detect a significant result, it should be a pertinent subject within these studies. Only four articles were located which had
discussed, or at least referred to, power. Of these, one indicated a 0.80 power level, which is the suggested level indicating
the probability that the analytical tests will yield statistically significant results if the phenomena truly exist (Cohen 1977) while
maintaining a Type I error level.
Chin, Marcolin and Newsted
24
Table 1. Summary of Analysis of Variance Techniques
Sample Size Significant Sample Size Significant Sample Size Significant
Moderators* Moderators* Moderators*
73/3 132 2/6 48 2/43
441/387 2/22 359 4/4 1459 1/4
105 0/5 120 1/3 30 1/4
313,254 0/1 141 1/8 363 1/8
n/a 2/4 36 1/3 83 0/2
n/a 2/14 288 1/3 79 1/2
114 0/1 70 1/2 18 1/2
24 0/1 90 1/3 21 1/9
287/255 0/2 599 2/10 53 1/1
40 3/3 72 0/2 173 1/9
28 0/2 1454 1/4 80 0/4
256 1/2 43 1/3 39/27 1/2
48 1/8 768 1/3 504 0/1
36 2/3 16/26/86/58 1/5 48 0/3
49 0/1 112 2/4 36 1/1
28 2/4
46 articles average sample size is 200 including articles with time series
51 samples average sample size is 149 excluding articles with time series
53/243 moderators had significant results
*n/m means n out of m moderators were found significant. For example, 2/43 means 2 out of 43 moderators
tested were significant
Low power may have been a main culprit in the large number of non-significant results found in the review. Low precision
(i.e., larger standard error) in the analytic calculations can be impacted by small sample sizes, random measurement error, and
the shape of the data distributions. Sample sizes averaged 81 for articles using regression or path analysis, and 149 for articles
using analysis of variance (see Tables 1 and 2). Given the fact that the greater the precision, the greater the probability of
detecting a significant result, one wonders whether these studies reviewed had enough power to detect an effect if it existed.
It is possible, given the average sample sizes, that many unknown interaction effects were left undetected.
Thus, moderators have been used to some extent in the IS field, but have generally been difficult to detect. Few studies have
used analytic techniques that actually calculate the effect size; power levels tend to be low; and meta-analyses are either
theoretical (Trice and Treacy 1986; Goodhue 1986) or report inconsistent results (Cavaye 1995). The inconsistent results in
the meta-analyses are often blamed on different operationalizations of the constructs, uncontrolled research factors,
inappropriate quantitative studies with little richness in the understanding of the influences, and poorly validated instruments
(Cavaye 1995).
Regardless of the true effect of moderators, it can be concluded from the review that better reporting would drastically improve
the body of knowledge being built within the information systems field. Sample sizes, effect sizes, power of statistical tests,
and the usual significance levels (p=.05 or .01) are needed to provide consistency in the results.
A Partial Least Squares Latent Variable Modeling Approach
Additional information about the PLS method and how it compares to covariance based procedures is provided in
2
Appendix A.
25
Table 2. Summary of Regression and Path Analysis Articles
Sample Size Power Average Effect Size Number of
Number of (beta) significant
Indicators moderators*
36 no n/a n/a 0/1
30 no 5 unstandardized 3/4
30 no n/a split sample 2/4
249 n/a 3unstandardized 1/3
151 no 8 .03, .026 2/4
47 no 1 .26 1/3
77/32 .80 1unstandardized 3/3
average
81 3.4 12/22
*n/m means n out of m moderators were found significant. For example, 3/4 means
3 out of 4 moderators tested were significant
Given the current state of the literature concerning IS moderating variables, in the remaining sections of this paper we try to
make improvements. A new latent variable modelling approach for analyzing interaction effects is first offered, and the
technique is then supported with evidence from a simulated data set and an IT adoption data set.
3. PARTIAL LEAST SQUARES PRODUCT INDICATOR APPROACH
FOR MEASURING INTERACTION
To account for the deleterious effects of measurement error, a product indicator approach in conjunction with Partial Least
Squares (PLS) is proposed. The predictor, moderator, and dependent variables are now viewed as latent variables (i.e.,
constructs) which cannot be measured directly. Instead, multiple indicators (i.e., measures) for these latent variables need to
be obtained. Each indicator is modeled as being influenced by both the underlying latent variable and error. Product indicators
reflecting the latent interaction variables are then created. Each set of indicators reflecting their underlying construct (i.e.,
latent variable) are then submitted to PLS for estimation resulting in a more accurate assessment of the underlying latent
variables and their relationships.
The PLS procedure has been gaining interest and use among IS researchers in recent years (Compeau and Higgins 1995;
Aubert, Rivard and Paltry 1994; Chin and Gopal 1995) because of its ability to model latent constructs under conditions of non-
normality and small to medium sample sizes. Being a components-based structural equations modeling technique, PLS is
similar to regression, but simultaneously models the structural paths (i.e., theoretical relationships among latent variables) and
measurement paths (i.e., relationships between a latent variable and its indicators). Rather than assume equal weights for all
indicators of a scale, the PLS algorithm allows each indicator to vary in how much it contributes to the composite score of the
latent variable. Thus indicators with weaker relationships to related indicators and the latent construct are given lower
weightings. In this sense, PLS is preferable to techniques such as regression which assume error free measurement (Lohmöller
1989; Wold 1982, 1985, 1989).2
Chin, Marcolin and Newsted
The effect size f = [R (interaction model) - R (main effects)] / R (interaction model).
3 2 2 2 2
The results presented in this paper used standardized indicators. Similar results were obtained when we centered them.
4
26
Under assumptions of error free measurement, product term regression analysis is generally recommended for continuous
variables to detect interaction effects (Jaccard, Turrisi, and Wan 1990; Cohen and Cohen 1983). Yet, for variables that are
measured with error (i.e., latent variables), regression produces biased and inconsistent coefficient estimates along with a loss
of statistical power as the reliability of the measures decline (Busemeyer and Jones 1983; Aiken and West 1991). For example,
Aiken and West (p. 164) show that while a sample of about 400 is needed to achieve a power of 0.80 to detect a small effect
(f = 0.02) with perfect measures, sample requirements increase to 1,056 if the reliability of the measure is 0.80. In general,
2 3
the power to detect an interaction effect at a given sample size is reduced by up to one half when reliabilities are 0.80 rather
than 1.00 and up to two thirds when reliabilities decrease to 0.70. In addition, the estimates of the interaction effect sizes can
also be significantly reduced as reliability decreases (Aiken and West, p. 161).
In addressing these problems, we apply a product indicator approach in conjunction with the PLS procedure to estimate the
underlying interaction construct. Under the traditional regression based approach for modeling interaction effects, a single
product term is used (x*z) to examine the influence that a moderator z would have on the relationship between the predictor
x and the dependent variable of interest y. Yet, as discussed earlier, this approach is made under the assumption that each
measure is error free. To account for the condition of measurement error, we can view the independent variables x, z, and x*z
as indicators which reflect the true underlying continuous latent constructs of interest. The estimation of this true underlying
construct, in turn, entails the use of multiple/parallel indicators.
First, multiple indicators of the underlying constructs (i.e., reflecting X, Z, and Y), need to be obtained. The predictor (X) and
moderator (Z) indicators are then used to create product indicators. To do this, we need to determine whether the individual
indicators for X and Z are theoretically parallel measures or if some are more important based on their measurement scale
and/or variance. For the first scenario, we consider the indicators for each construct to be approximately equivalent and do
not give any more credence to any one particular indicator in a set. Under this condition, we would standardize all indicators
reflecting the predictor and moderator constructs to a mean of zero and variance of one (Jaccard, Turrisi, and Wan 1990; Aiken
and West 1991). This approach would be reasonable for ordinal to interval level items such as Likert scaled attitude items.
Alternatively, one would center the indicators to a mean of zero if it is felt the original metric of the items or the variances
should be maintained. For ratio level items, it is important to have all items transformed to the same metric in addition to
4
being centered. Otherwise, the estimated latent variable score produced by PLS would be indeterminable.
Standardizing or centering the indicators helps avoid computational errors by lowering the correlation between the product
indicators and their individual components (Smith and Sasaki 1979). Furthermore, without such a process, each product term
would likely have a different location parameter leading to an inability for the PLS procedure to accurately estimate the
underlying interaction construct. It also allows us an easier interpretation of the resulting regression beta for the predictor
variable; that being the effect we would expect at the average value of the moderator variable (which is centered to zero).
Standardizing is accomplished by calculating the mean and s.d. for each indicator. Then for each indicator score, the
corresponding mean is subtracted and divided by the respective s.d. Centering refers only to subtracting the mean.
Using the standardized or centered indicators of the predictor variable (i.e., X) and the moderator variable (i.e., Z), product
indicators are then developed by creating all possible products from the two sets of indicators. These product indicators are
used to reflect the latent interaction variable. For example, if we have three measures reflecting the main predictor (X) and
three measures for the moderator variable (Z), we would have nine measures for representing the interaction term (X*Z).
Graphically, this is depicted in Figure 1. Since any indicator reflecting the predictor (X) or moderator (Z) is viewed as
interchangeable with another from the same set, any product indicator (x *z) would represent an equivalent representation of
i i
the underlying latent interaction variable (X*Z).
The PLS procedure is then used to estimate the latent variables as an exact linear combination of its indicators with the goal
of maximizing the explained variance for the indicators and latent variables. Following a series of ordinary least squares
A Partial Least Squares Latent Variable Modeling Approach
For standardized indicators, the default estimation procedure of unit variance/no location should yield similar results to
5
the original scale/with locations option. For centered data, the original scale/with locations should be used.
We should noted that what we conclude regarding effects size estimations using regression throughout this paper is equally
6
or more so for ANOVA since the latter represents a special case of the former.
27
analyses, PLS optimally weights the indicators such that a resulting latent variable estimate can be obtained. The weights
5
provide an exact linear combination of the indicators for forming the latent variable score which is not only maximally
correlated with its own set of indicators (as in components analysis), but also correlated with other latent variables according
to the structural (i.e. theoretical) model.
It should be noted that the underlying assumption of uncorrelated error terms among the indicators is not true (see Kenny and
Judd [1984] for derivation). The error terms for the product indicators are partially correlated with the error terms associated
with the indicators of the other exogenous constructs. Thus, the estimation procedure using PLS might be affected. The extent
to which this is problematic will be assessed in the next section.
4. STUDY 1: MONTE CARLO SIMULATION
To test the efficacy of the Partial Least Squares– product indicator approach for detecting and estimating interaction effects
where measurement error exists, we ran a Monte Carlo simulation study varying the sample size and number of indicators.
Data were created using PRELIS 2.14 (Jöreskog and Sorbom 1993), to conform to an underlying population model where the
standardized beta from X to Y is 0.3, the beta of Z on Y is 0.5, and the interaction effect is 0.3. Indicators for all primary
constructs (i.e., latent variable) were modeled to have factor loadings of 0.70. Thus, we know what are to be the main and
interaction effects. The goal here is to determine how good the PLS-product indicator approach is at detecting and recovering
(i.e., estimating) the true effects under conditions of measurement error.
The two treatments considered were sample size and number of indicators per construct (i.e., latent variable). Sample sizes
consisted of 20, 50, 100, 150, 200, and 500. Number of indicators per primary construct (i.e., X, Z, and Y) varied as follows:
1, 2, 4, 6, 8, 10, and 12. For each treatment cell, one hundred simulations were performed. Thus, for example, in the cell
representing sample size 50 and three indicators per construct, we generated 100 data sets consisting of sample sizes of 50
where each case had three indicators for each of the three constructs X, Z, and Y respectively and nine product indicators for
X*Z.
Table 3 provides the path and standard error results of our 6 by 7 study where PLS runs were made using PLS-Graph version
2.9 (Chin 1994). Our basis for how well the PLS-product indicator approach performed is multiple regression. The results of
using multiple regression over varying sample sizes is provided in the column labeled single item per construct. When using
PLS, this limiting case of one indicator per construct is identical to performing a multiple regression.
Keeping in mind that a perfect estimation procedure should result in 0.30 (x to y), 0.50 (z to y), and 0.30 (x*z to y), the results
using multiple regression under conditions of measurement error consistently underestimated the true effects. The reason, as
discussed earlier, is that regression does not explicitly take into account the attenuating effects of measurement error. At a
6
sample size of 500, for example, the estimation are at a half to one quarter of the real effects. Larger sample size, while
providing smaller standard errors, did not result in closer approximations to the true effects.
The results do show that for any sample size, as the number of indicators increased, the estimation tended to move closer to
the true effect. For example, at sample size 100, the estimation of the interaction effect approached the true effect of 0.30 at
eight or more indicators. The estimation for the moderator z, while never reaching the true effect, increased until it reached
an asymptotic limit at eight indicators.
X
Predictor
Variable
X*Z
Interaction
Effect
x1 x2 x3
Z
Moderator
Variable
z1 z2 z3
Y
Dependent
Variable
y1 y2 y3
x2*z1 x2*z2 x2*z3 x3*z1 x3*z2 x3*z3x1*z1 x1*z2 x1*z3
Chin, Marcolin and Newsted
28
Figure 1. Model with Three Indicators per Main Constructs and Nine Product
Indicators for the Interaction Construct
Table 3. Results of Monte Carlo Simulation (100 Runs per Cell)
Indicators per construct
Sample size single item per two per construct (4 four per construct six per construct (36 eight per construct ten per construct (100 twelve per construct
construct for interaction) (16 for interaction) for interaction) (64 for interaction) for interaction) (144 for interaction)
20 (0.2462) (0.2340) (0.2430) (0.2160) (0.2150) (0.2332) (0.2083)
x -->y 0.1449 x -->y 0.2177 x -->y 0.2070 x -->y 0.2352 x -->y 0.2237 x -->y 0.2391 x -->y 0.2450
z --> y 0.2898 z --> y 0.3113 z --> y 0.3307 z --> y 0.3168 z --> y 0.3204 z --> y 0.3176 z --> y 0.3622
(0.2262) (0.2296) (0.2136) (0.2037) (0.2286) (0.2232) (0.1665)
x*z--> y 0.1458 x*z--> y 0.1609 x*z--> y 0.2708 x*z--> y 0.1897 x*z--> y 0.1988 x*z--> y 0.2788 x*z--> y 0.3557
(0.2852) (0.3358) (0.3601) (0.4169) (0.4399) (0.3886) (0.3725)
50 (0.1442) (0.1506) (0.1434) (0.1294) (0.1523) (0.1341) (0.1090)
x -->y 0.1008 x -->y 0.2155 x -->y 0.2279 x -->y 0.2521 x -->y 0.2593 x -->y 0.2548 x -->y 0.2694
z --> y 0.2409 z --> y 0.3120 z --> y 0.3914 z --> y 0.3751 z --> y 0.3941 z --> y 0.3885 z --> y 0.4160
(0.1276) (0.1320) (0.1013) (0.1106) (0.1011) (0.1089) (0.0999)
x*z--> y 0.1133 x*z--> y 0.1142 x*z--> y 0.2795 x*z--> y 0.2403 x*z--> y 0.3066 x*z--> y 0.3083 x*z--> y 0.3615
(0.1604) (0.2124) (0.1873) (0.2795) (0.2183) (0.2707) (0.1848)
100 (0.0925) (0.0828) (0.0836) (0.0901) (0.0859) (0.0789) (0.0776)
x -->y 0.1461 x -->y 0.2129 x -->y 0.2605 x -->y 0.2674 x -->y 0.2716 x -->y 0.2716 x -->y 0.2805
z --> y 0.2453 z --> y 0.3070 z --> y 0.3747 z --> y 0.4090 z --> y 0.4354 z --> y 0.4354 z --> y 0.4308
(0.0868) (0.0821) (0.0727) (0.0870) (0.0638) (0.0724) (0.0724)
x*z--> y 0.1012 x*z--> y 0.1614 x*z--> y 0.2472 x*z--> y 0.2669 x*z--> y 0.3029 x*z--> y 0.3029 x*z--> y 0.3008
(0.0989) (0.1276) (0.1270) (0.1301) (0.0916) (0.0805) (0.1352)
150 (0.0779) (0.0627) (0.0623) (0.0661) (0.0600) (0.0623) (0.0563)
x -->y 0.1459 x -->y 0.2078 x -->y 0.2478 x -->y 0.2609 x -->y 0.2704 x -->y 0.2711 x -->y 0.2862
z --> y 0.2474 z --> y 0.3251 z --> y 0.4007 z --> y 0.4156 z --> y 0.4424 z --> y 0.4466 z --> y 0.4530
(0.0713) (0.0768) (0.0540) (0.0583) (0.0598) (0.0587) (0.0514)
x*z--> y 0.0953 x*z--> y 0.1695 x*z--> y 0.2427 x*z--> y 0.2834 x*z--> y 0.2805 x*z--> y 0.3040 x*z--> y 0.2921
(0.0843) (0.0844) (0.0778) (0.0757) (0.0916) (0.0567) (0.0840)
200 (0.0601) (0.0670) (0.0596) (0.0509) (0.0460) (0.0542) (0.0506)
x -->y 0.1625 x -->y 0.1919 x -->y 0.2327 x -->y 0.2559 x -->y 0.2688 x -->y 0.2687 x -->y 0.2814
z --> y 0.2458 z --> y 0.3289 z --> y 0.3985 z --> y 0.4184 z --> y 0.4368 z --> y 0.4533 z --> y 0.4601
(0.0644) (0.0611) (0.0550) (0.0550) (0.0541) (0.0527) (0.0509)
x*z--> y 0.0962 x*z--> y 0.1769 x*z--> y 0.2317 x*z--> y 0.2730 x*z--> y 0.2839 x*z--> y 0.2843 x*z--> y 0.3018
(0.0785) (0.0674) (0.0543) (0.0528) (0.0606) (0.0573) (0.0542)
500 (0.0450) (0.0388) (0.0385) (0.0373) (0.0350) (0.0359) (0.0381)
x -->y 0.1425 x -->y 0.1926 x -->y 0.2426 x -->y 0.2595 x -->y 0.2731 x -->y 0.2778 x -->y 0.2773
z --> y 0.2421 z --> y 0.3339 z --> y 0.3960 z --> y 0.4221 z --> y 0.4396 z --> y 0.4553 z --> y 0.4574
(0.0463) (0.0364) (0.0353) (0.0349) (0.0373) (0.0335) (0.0316)
x*z--> y 0.0965 x*z--> y 0.1681 x*z--> y 0.2275 x*z--> y 0.2448 x*z--> y 0.2637 x*z--> y 0.2659 x*z--> y 0.2761
(0.0436) (0.0358) (0.0419) (0.0379) (0.0377) (0.0353) (0.0375)
x-->y refers to the mean of 100 path estimates from predictor x to criterion y (standard errors within parenthesis).
z-->y refers to the mean of 100 path estimates from the moderator variable z to criterion y (standard errors within parenthesis).
x*z-->y refers to the mean of the 100 path estimates for the interaction effect of z on the path from x to y (standard errors within parenthesis)
Chin, Marcolin and Newsted
30
Sample size, in general, did not influence the consistency of the estimation. Estimates tended to be quite similar for any
column of Table 3. What sample size does influence instead is the ability to detect an effect which is reflected in the variation
of the estimates.
Table 4. Tests of Significance for the Mean Estimates (100 Runs)
Number of Inidcators
Predictor: x
1 2 4 6 8 10 12
Sample Size
20
50 * * * **
100 ** ** ** ** ** **
150 0 ** ** ** ** ** **
200 ** ** ** ** ** ** **
500 ** ** ** ** ** ** **
Moderator: z
1 2 4 6 8 10 12
Sample Size
20 *
50 0 ** ** ** ** ** **
100 ** ** ** ** ** ** **
150 ** ** ** ** ** ** **
200 ** ** ** ** ** ** **
500 ** ** ** ** ** ** **
Interaction: x*z
1 2 4 6 8 10 12
Sample Size
20
50 *
100 * * ** ** *
150 * ** ** ** ** **
200 ** ** ** ** ** **
500 0 ** ** ** ** ** **
*p < .05 (One-tailed t value: 1.66, df = 99)
** p < .01 (One-tailed t value: 2.36, df = 99)
A Partial Least Squares Latent Variable Modeling Approach
31
In the case of multiple regression, for example, the ability to detect a beta effect of 0.30 (predictor X situation) did not occur
until sample size 150 (see Table 4). But if we up the beta to a 0.50 effect, as in the case for moderator Z, significance occurred
at a size of 50. If the effect size remained at 0.30, but the reliability drops in half (as in the case for the interaction effect
where its reliability is the product of reliabilities of X and Z) only the sample of size of 500 was large enough. Until then, the
standard errors relative to the estimated effect sizes were too large.
Table 4 also shows how increasing indicators will increase power. This is clearest for the interaction effect where a significant
effect at the 0.01 level was obtained either at a larger sample size of 150 with four to six indicators or at a smaller size of 100
with eight indicators. For the more reliable predictor x (with similar effect size), significant detection at the 0.01 level was
obtained for two indicators at a larger sample size 100 or twelve indicators at a smaller size of 50. When the effect size is
larger (i.e., moderator z), a sample size of 100 is needed for detection using multiple regression or a smaller size of 50 with
two or more indicators using PLS.
This simulation, therefore, partially demonstrates what Wold (1985, 1989) termed consistency at large for PLS estimation.
This means that PLS estimation tends toward the true population parameter as the number of indicators and sample size
increase.
We also see how measurement error, in the case of multiple regression, can attenuate the true effect and leave the IS researcher
with the impression that an interaction effect is much smaller than it really is or possibly non-existent. The interaction estimate,
in particular, would generally represent the worst among the estimations since its reliability is the product of the reliabilities
of its predictor and moderator indicators.
Table 5 represents yet another side of the consistency at large influence in PLS estimation. While the loadings should ideally
be estimated at the true value of 0.70 for main effects constructs and 0.49 for the interaction construct, it is a known fact that
PLS tends to underestimate the structural paths connecting constructs to one another and overestimates the measurement paths
connecting constructs to their indicators (Chin 1995). If we ignore the loadings for those situations in Table 4 that yielded non-
significant estimations, we can see that the loadings tend to be inflated by more than ten percent in the two and four indicator
situation. And as conjectured by Chin (1995, p. 319), it is not until we use ten to twelve indicators that an asymptotic limit
is reached.
Other effect sizes and loadings should be tested in the future to get an even greater appraisal of how PLS estimates can vary.
In the scenario we examined, it would suggest that a minimum sample size of 100 is needed in order to detect the interaction
effect and six to eight indicators per construct to obtain structural path estimates within 10 percent of the true effects. This
conclusion, in marked contrast to our earlier literature review that indicated the average sample size was 81 and number of
indicators at 3.4, may provide a possible reason for the poor results of past IS studies.
5. STUDY 2: THE MODERATING EFFECT OF ENJOYMENT ON THE PERCEIVED
USEFULNESS/IT ADOPTION INTENTION RELATIONSHIP
In this section, the PLS-product indicator approach is applied to detecting the interaction effect of enjoyment on the perceived
usefulness/IT adoption intention relationship. Recall at the beginning of this paper, we had used the Technology Acceptance
Model (Davis 1989) as the context for an example of an interaction effect. The same context will now be used as a test case.
In the original model, perceived usefulness and perceived ease of use was modeled as having direct effects on adoption
intention.
Davis, Bagozzi, and Warshaw (1992) note the difference between extrinsic and intrinsic sources of motivation to use computers
in the workplace. They found that perceived usefulness, an extrinsic source of motivation, had a large significant effect on
adoption intention as expected. However, its influence was complemented by enjoyment, an intrinsic source of motivation
defined as the extent to which the activity of using the computer is perceived to be enjoyable in its own right, apart from any
performance consequences. They also found that both variables mediated the influence of perceived ease of use on intention.
Thus, perceived ease of use was not included in predicting intention for this analysis.
Chin, Marcolin and Newsted
Average refers to taking the mean of the loadings (100 runs) for each indicator connected to a construct and then
7
calculating the means. The number of indicators for the interaction construct is the square of the number of indicators for the
predictor and moderate constructs.
32
Table 5. Average Loadings for Each Construct7
sample size XZX*Z
two indicators
20 0.758 0.809 0.570
50 0.793 0.825 0.617
100 0.827 0.848 0.635
150 0.841 0.859 0.656
200 0.853 0.862 0.703
500 0.857 0.861 0.729
four indicators
20 0.672 0.715 0.416
50 0.729 0.764 0.536
100 0.767 0.782 0.564
150 0.773 0.782 0.581
200 0.781 0.781 0.585
500 0.783 0.785 0.612
six indicators
20 0.698 0.726 0.390
50 0.716 0.744 0.466
100 0.743 0.757 0.512
150 0.752 0.757 0.547
200 0.754 0.756 0.555
500 0.756 0.756 0.571
eight indicators
20 0.672 0.685 0.415
50 0.690 0.735 0.475
100 0.736 0.739 0.510
150 0.741 0.744 0.538
200 0.738 0.740 0.537
500 0.745 0.745 0.554
ten indicators
20 0.656 0.704 0.402
50 0.699 0.726 0.456
100 0.714 0.737 0.513
150 0.725 0.731 0.510
200 0.731 0.734 0.524
500 0.735 0.736 0.537
twelve indicators
20 0.667 0.693 0.395
50 0.694 0.723 0.473
100 0.703 0.726 0.484
150 0.728 0.728 0.520
200 0.730 0.732 0.535
500 0.728 0.730 0.530
Dc'(
j
8i)2varF
(j8i)2varF %j1ii
A Partial Least Squares Latent Variable Modeling Approach
The authors wish to acknowledge Stephen Hayne for establishing contact with the organization and assisting in the
8
delivery and receipt of the surveys.
33
Chin and Gopal similarly found both enjoyment and relative advantage (identical items to perceived usefulness) had a direct
effect on Group Support System adoption intentions. In their article, they state “that there is also the possibility of interaction
effects among the constructs that were not taken into account in this study. For example, Davis, Bagozzi and Warshaw indicate
that a positive interaction may exist between enjoyment and usefulness. Because of its similarity to usefulness, the relative
advantage construct used in this study may also have an interaction effect with enjoyment” (p. 58).
In order to test the possibility of such an interaction effect, the perceived usefulness and enjoyment items were used to examine
the adoption intention of electronic mail (see Appendix B for construct definition and items used). The data were obtained
from a single organization that had recently installed electronic mail. A total of sixty questions relating to a recent
8
introduction of electronic mail were presented. Of the 575 questionnaires distributed, 250 usable responses were analyzed
representing 43.5 percent of the those surveyed. On average, the respondents had been using electronic mail for nine months,
sent 2.53 messages per day (s.d. = 2.36) and received 4.79 messages per day (s.d. = 3.49). Respondents were on average 39
years old (s.d. = 9.28) and had worked for the company an average of eleven years (s.d. = 6.9). Of the respondents, 60 percent
were were male. The respondents came from various levels in the organization, 13 percent were managers, 12 percent were
engineers, 38 percent were technicians, and the remaining 37 percent were clerical workers.
The results (see Figure 2) give a standardized beta of 0.449 from usefulness to intention, 0.227 from enjoyment to intention,
and an interaction effect of -0.209 with a total R-square of 0.50. Thus, these results imply that one standard deviation increase
in enjoyment will not only impact intention by 0.227, but it would also decrease the impact of perceived usefulness to intention
from 0.449 to 0.240. The main effects model (see Figure 3), as expected, resulted in slightly higher standardized beta and a
smaller R-square of 0.465. The interaction effect, therefore, has an effect size f of 0.07 which is between a small and medium
effect (Cohen and Cohen 1983) and represents about twice the average for past IS studies. More importantly, the beta estimates
suggest the conditions under which enjoyment becomes a dominant factor equaling and potentially overshadowing perceived
usefulness, that being for the group of people who perceive electronic mail to be extremely enjoyable.
To assess whether the interaction effect and main effects were significant, a bootstrap resampling procedure (Efron and
Tibshirani 1993) was performed. The results of 200 resamples indicate that all paths, weights, and loadings (see Table 6) were
significant at the 0.01 level.
We next need to assess how accurate the path estimates are to the “true” effect. As noted earlier, the estimates of the structural
paths tend to be more accurate as the reliability of the estimated construct score increases. To assess the reliability of the latent
variable estimated by PLS, the composite reliabilities as suggested by Werts, Linn, and Jöreskog (1974) were calculated and
presented in Table 6. While Cronbach’s alpha with its assumption of parallel measures represents a lower bound estimate of
internal consistency, a better estimate can be gained using the composite reliability formula. The composite reliability D is
c
defined as:
where 8, F, and 1, are the factor loading, factor variance, and unique/error variance respectively. For our PLS analysis using
i ii
unit variance scaling procedures, 8 is given in Table 6, F is set at 1, and 1 is 1 minus the square of 8. Using this formula,
i ii i
which does not assume a tau equivalency among the measures, typically provides more accurate estimates of the composite
reliability. Overall, except for enjoyment with a three indicator composite reliability of 0.85, the composite reliabilities of the
other constructs are very high (at or above 0.96). In the case of enjoyment, if we take the composite reliability as a bias
correction factor, the 0.227 path between enjoyment and intention would increase slightly to 0.246.
0.227
-0.209
0.449
Intention To
Regularly Use
Electronic
Mail
Perceived
Usefulness
Enjoyment
Usefulness X
Enjoyment
R-Square = 0.50
0.269
0.517 Intention To
Regularly Use
Electronic
Mail
Perceived
Usefulness
Enjoyment
R-Square = 0.465
Chin, Marcolin and Newsted
34
Figure 2. Results of the Interaction Model
Figure 3. Results of the Main Effects Model
6. DISCUSSION AND CONCLUSION
This paper has provided a new approach toward the assessment of interaction effects among continuous variables. As Cronbach
(1987, p. 417) has urged, “further investigation of statistical power in studies of interaction and invention of more sensitive
research strategies are much to be desired.” Using simulated data, we were able to provide an initial sense as to the efficiency
and effectiveness of this approach. In general, assuming the true average loading is 0.70, sample sizes of approximately 100
are needed in order to detect the interaction effect with six to eight indicators per main effects constructs to yield reasonably
consistent estimates. Under smaller sample sizes or number of indicators, the known bias in PLS for overestimating the
measurement loading and underestimating the structural paths among constructs may occur. Yet, it is possible that with more
reliable measures (e.g., true loadings of 0.80), the need for six to eight indicators per construct may be relaxed as well as the
sample size.
A Partial Least Squares Latent Variable Modeling Approach
35
Table 6. Weights and Loadings Results from Overall, more simulation studies need to be done under
PLS Analysis (Interaction Model) for Study 2 varying conditions to assess how PLS in general and the
ITEM WEIGHT LOADING
Perceived Usefulness
composite reliability = 0.975
UFL1 0.175 0.890
UFL2 0.166 0.934
UFL3 0.179 0.951
UFL4 0.183 0.958
UFL5 0.177 0.944
UFL6 0.196 0.904
Enjoyment
composite reliability = 0.853
ENJ1 0.463 0.907
ENJ2 0.488 0.867
ENJ3 0.244 0.645
Intention
composite reliability = 0.964
INT1 0.329 0.945
INT2 0.362 0.949
INT3 0.364 0.949
Interaction
composite reliability = 0.980
UFL1ENJ1 0.079 0.890
UFL1ENJ2 0.070 0.848
UFL1ENJ3 0.063 0.831
UFL2ENJ1 0.068 0.878
UFL2ENJ2 0.065 0.828
UFL2ENJ3 0.050 0.802
UFL3ENJ1 0.070 0.906
UFL3ENJ2 0.064 0.842
UFL3ENJ3 0.050 0.813
UFL4ENJ1 0.071 0.903
UFL4ENJ2 0.069 0.882
UFL4ENJ3 0.050 0.836
UFL5ENJ1 0.072 0.908
UFL5ENJ2 0.067 0.873
UFL5ENJ3 0.052 0.829
UFL6ENJ1 0.079 0.878
UFL6ENJ2 0.074 0.843
UFL6ENJ3 0.053 0.789
PLS–product indicator approach in particular performs.
While the ability to detect and obtain consistent estimates
will likely occur sooner with more reliable measures, it is
not clear how the procedure will work for a nonhomoge-
neous set of indicators where the loadings vary as well as
the degree of normality. Based on our understanding of the
PLS algorithm, we would expect it to perform better than a
strategy of simply summing the individual indicators to
create a composite score and using multiple regression.
While the sample size suggested here may seem quite large,
it is relatively small when contrasted to the sample size
necessary for covariance based such as LISREL or EQS
approached. As an extreme, consider the case of twelve
indicators per construct. This represents, as a first approxi-
mation, 364 parameters to be estimated (180 factor loadings,
180 error terms, three structural paths, and one endogenous
error term). While a power analysis or simulation study
provides us with a more accurate means for estimating the
necessary sample size, Bentler and Chou (1988, p. 172)
gave a heuristic of five cases per parameter estimated under
normal or elliptical conditions. Using this rule, we would
need a sample size of 1,820. Even for the simpler two
parameter per construct case, you would still need a sample
size of 120. For non-normal conditions, Bentler and Chou
recommend a minimum ratio of ten cases per parameter
estimated.
Using an actual data set, we demonstrated the interaction
effect between enjoyment and perceived usefulness on
adoption intention. With the simulation study as a guide, it
is likely that the structural effects are still being underesti-
mated and the construct loadings are being overestimated
since the number of indicators for the two constructs were
three and six respectively. But in this case, using a 10
percent inflation rule, the true loadings are likely higher
since the estimates are in the 0.90 region. The extent to
which the negative moderating effect of enjoyment holds up
in future studies is debatable, but the results do suggest the
need for further research regarding the role of emotions in
general and enjoyment in particular for predicting IT
intentions and usage behaviors.
The approach presented here of creating nonlinear product indicators for PLS estimation can be extended to the other powers
(e.g., X, X , or X *Z) as long as the indicators for the predictor and moderator constructs are viewed as reflective measures.
2 3 2
Further, the indicators need not be interval level. We believe that ordinal or even dichotomous variables can be used as long
as there is a large enough set to represent the underlying continuous latent variable.
Chin, Marcolin and Newsted
36
Ideally, additional power constructs for the main components (i.e., X and Z ) should be included with the interaction construct
2 2
in a stepwise regression fashion. Assuming equivalent composite reliabilities, having the product construct enter first relative
to the other constructs would be indicative of an interaction effect. Without such a process, we cannot conclusively attribute
the effect to the interaction term. Due to page limitations, we did not perform this with the Study 2 data since the goal of this
paper was to demonstrate our new approach.
The current procedure cannot be used for formative indicators which are viewed as measures that create a latent construct (see
Chin and Gopal for a good discussion regarding the formative/reflective distinction). One approach for formative indicators
would be to follow a two step construct score procedure. The first step would entail using the formative indicators in
conjunction with PLS to create underlying construct scores for the predictor and moderator variables. Step two would then
consist of taking those single composite scores to create a single interaction term.
In summary, we hope this new approach will yield stronger results for future researchers interested in assessing interaction
effects. Furthermore, it is hoped that issues such as appropriate sample size, multiple indicators, and power will be part of the
standard information provided in future research, which should help the IS field build a more cumulative knowledge base than
what we found in our literature review.
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A Partial Least Squares Latent Variable Modeling Approach
39
APPENDIX A: PLS METHOD
Partial Least Squares (PLS) can be a powerful method of analysis because of the minimal demands on measurement scales,
sample size, and residual distributions. Although PLS can be used for theory confirmation, it can also be used to suggest where
relationships might or might not exist and to suggest propositions for later testing.
As an alternative to the more widely known covariance fitting approach (exemplified by software such as LISREL, EQS,
COSAN, AMOS, and SEPATH), the component-based PLS avoids two serious problems: inadmissible solutions and factor
indeterminacy (Fornell and Bookstein 1982). The philosophical distinction between these approaches is whether to use
structural equation modeling for theory testing and development or for predictive applications (Anderson and Gerbing 1988).
In situations where prior theory is strong and further testing and development is the goal, covariance based full-information
estimation methods (i.e., Maximum Likelihood or Generalized Least Squares) are more appropriate. Yet, due to the
indeterminacy of factor score estimations, there exists a loss of predictive accuracy. This, of course, is not of concern in theory
testing where structural relationships (i.e., parameter estimation) among concepts is of prime concern.
For application and prediction, a PLS approach is often more suitable. Under this approach, it is assumed that all the measured
variance is useful variance to be explained. Since the approach estimates the latent variables as exact linear combinations of
the observed measures, it avoids the indeterminacy problem and provides an exact definition of component scores. Using an
iterative estimation technique (Wold 1982), the PLS approach provides a general model which encompasses, among other
techniques, canonical correlation, redundancy analysis, multiple regression, multivariate analysis of variance, and principle
components.
As a consequence of using an iterative algorithm consisting of a series of ordinary least squares analyses, identification is not
a problem for recursive (i.e., one way path) models nor does it presume any distributional form for measured variables.
Furthermore, sample size can be smaller, with a standard rule of thumb suggesting that it be equal to the larger of the following:
(1) ten times the scale with the largest number of formative (i.e., causal) indicators (note that scales for constructs designated
with reflective indicators can be ignored), or (2) ten times the largest number of structural paths directed at a particular
construct in the structural model. A weak rule of thumb, similar to the heuristic for multiple regression (Tabachnik and Fidell
1989, p. 129), would be to use a multiplier of five instead of ten for the preceding formulae. An extreme example is given by
Wold (1989), who analyzed 27 variables using two latent constructs with a data set consisting of ten cases.
When estimating interaction effects, Ping (1996) noted that recent covariance based procedures “can produce specification
tedium and errors or estimation difficulties in larger structural equations models.” Ping (1995; 1996) has suggested an
alternative two-step approach to overcome these limitations, however the ability to assess the reliability and validity of
individual items using a two step approach has been questioned (Fornell and Yi 1992).
Second order factors can be approximated using various procedures. One of the easiest to implement is the approach of
repeated indicators known as the hierarchical component model suggested by Wold (cf. Lohmöller 1989, pp. 130-133). In
essence, a second order factor is directly measured by observed variables for all the first order factors. While this approach
repeats the number of manifest variables used, the model can be estimated by the standard PLS algorithm. This procedure
works best with equal numbers of indicators for each construct.
Finally, PLS is considered better suited for explaining complex relationships (Fornell, Lorange, and Roos 1990; Fornell and
Bookstein 1982). As stated by Wold (1985, p. 589), “PLS comes to the fore in larger models, when the importance shifts from
individual variables and parameters to packages of variables and aggregate parameters.” Wold states later (p. 590), “In large,
complex models with latent variables PLS is virtually without competition.”
Nevertheless, being a limited information method, PLS parameter estimates are less than optimal regarding bias and
consistency. The estimates will be asymptotically correct under the joint conditions of consistency (large sample size) and
consistency at large (the number of indicators per latent variable becomes large). Otherwise, construct to loadings tend to be
overestimated and structural paths among constructs underestimated. Furthermore, standard errors need to be estimated via
resampling procedures such as jackknifing or bootstrapping (cf. Efron and Gong 1983). The significance of paths can also be
determined by using the jackknife statistics resulting from a blindfolding resampling procedure (Lohmöller 1984, pp. 5-09
Chin, Marcolin and Newsted
40
through 5-12). The blindfolding procedure omits a part of the data matrix for the construct being examined and then estimates
the model parameters. This is done a number of times based on the blindfold omission distance. Results obtained from this
resampling procedure include the jackknifed estimated means and standard deviations.
In this paper, all structural paths were significant at the 0.01 level using a bootstrapping sample of 200. Also, it should be noted
that by using the PLS algorithm under a reflective mode for all constructs, we eliminate any concerns of collinearity within
blocks of variables used to represent underlying constructs.
Overall, rather than being viewed as competitive models, the covariance fitting procedures (i.e., ML and GLS) and the
variance-based PLS approach have been argued as complementary in nature. According to Jöreskog and Wold (1982, p 270):
“ML is theory-oriented, and emphasizes the transition from exploratory to confirmatory analysis. PLS is primarily intended
for causal-predictive analysis in situations of high complexity but low theoretical information.”
APPENDIX B: CONSTRUCT DEFINITIONS AND
ITEMS USED FOR STUDY 2
Perceived Usefulness
Construct Definition (Davis 1989): The degree to which a system is perceived to enhance one’s performance.
UFL1 Using Electronic Mail in my job enables (would enable) me to accomplish tasks more quickly.
UFL2 Using Electronic Mail improves (would improve) my job performance.
UFL3 Using Electronic Mail in my job increases (would increase) my productivity.
UFL4 Using Electronic Mail enhances (would enhance) my effectiveness on the job.
UFL5 Using Electronic Mail makes it (would make it)easier to do my job.
UFL6 I find (would find) Electronic Mail useful in my job.
(Seven point scale using extremely likely, quite, slightly, neither, slightly, quite, extremely unlikely)
Future tense wording in parentheses were added to be meaningful for a percentage of respondents who have not used electronic
mail.
Enjoyment
Construct Definition (Davis, Bagozzi, and Warshaw 1992): The extent to which the activity of using the computer is perceived
to be enjoyable in its own right, apart from any performance consequences. (Electronic Mail was substituted for the behavior
of using the computer).
ENJ1 I find (would find) using Electronic Mail to be enjoyable.
(Seven point scale using extremely likely, quite, slightly, neither, slightly, quite, extremely unlikely)
ENJ2 The actual process of using Electronic Mail is (would be)
(Seven point scale using extremely unpleasant, quite, slightly, neither, slightly, quite, extremely pleasant)
ENJ3 I have (would have) fun using Electronic Mail.
(Seven point scale using extremely likely, quite, slightly, neither, slightly, quite, extremely unlikely)
A Partial Least Squares Latent Variable Modeling Approach
41
Intention To Regularly Use Electronic Mail
Construct Definition: A measure of the strength of one’s intention to perform a behavior [behavioral intention]. In this case,
the behavior is to use Electronic Mail regularly.
INT1 I presently intend to use Electronic Mail regularly:
(Seven point scale using extremely likely, quite, slightly, neither, slightly, quite, extremely unlikely)
INT2 My actual intention to use Electronic Mail regularly is:
(Seven point scale using extremely strong, quite, slightly, neither, slightly, quite, extremely weak)
INT3 Once again, to what extent do you at present intend to use Electronic Mail regularly:
(Eleven point scale from 0 to 10 with anchors Definite No, Definite Yes)
