Over the last decades, public agencies have been facing challenges in constraining expenditure for new transportation infrastructure projects or for the preservation of the aging infrastructure. This has led to innovative and cost-efficient technological advancements, which has in turn motivated the development of alternative funding methods that combine the public sector’s experience with the private entities’ capital investment and risk undertaking. Public–private partnerships (PPPs) for roadway construction and preservation constitute a rapidly growing type of synergy (contractual agreement) formed between public agencies and private sector entities (Engel et al., 2011). In fact, more than 46 billion dollars were disbursed between 1990 and 2010 in the USA for transportation PPP projects (Rall et al., 2010), while over 150 billion euros were allocated to PPP transportation projects in the European Union between 2000 and 2015 (Tomasi, 2016). Despite the widespread use of PPPs, the majority of public agencies have yet to determine a comprehensive decision making framework with respect to appropriate PPP type selection for a given transportation project. The need for such framework is corroborated by the frequent presence of critical project cost and time discrepancies during the implementation phase of PPP contracts.

Project cost and time discrepancies constitute contractual aberrations of high interest to both public and the private entities, and typically include cost overrun, cost savings, change orders, and time delays (Bordat et al., 2004). Previous research has been devoted on the investigation of the influential factors for each of the aforementioned project discrepancies, independently of the PPP type. The goal of this paper is to provide a comprehensive comparison of the parameters affecting contract discrepancies of popular PPP types, such as cost-plus-time (A + B),¹ performance-based contracting (PBC),² incentives/disincentives (I/D),³ design–build–operate–maintain (DBOM),⁴ lane rentals,⁵ and warranties⁶ (Mallet, 2008; Anastasopoulos et al., 2010a; Papajohn et al., 2010).

The identification of discrepancy- and PPP-specific relationships (i.e., identification of parameters specific to each discrepancy and PPP type) aims to assist transportation agencies in deciding whether a particular PPP type is appropriate for a specific roadway construction or preservation project, in terms of minimizing discrepancies and maximizing benefits.

A significant amount of past research in PPP projects for roadway construction and preservation has focused on the identification of factors affecting cost savings, cost overrun, time delays, and change orders (Rowland, 1981; Hester et al., 1991; Majid and McCaffer, 1998; Jacoby, 2001; Ellis and Thomas, 2003; Fimpong et al., 2003; Flyvbjerg et al., 2003; Bordat et al., 2004; Odeck, 2004; Assaf and Al-Hejji, 2006; Gkritza and Labi, 2008; Anastasopoulos et al., 2010a,b,c, 2011, 2014; Serag et al., 2010; Ambituuni, 2011; Irfan et al., 2011; Cantarelli et al., 2012). For example, Odeck (2004) formulated a regression framework to investigate the factors affecting cost overrun in roadway construction projects and found that small-scale projects are more vulnerable to cost overrun. The effect of the project size along with other significant contract attributes on cost savings and cost overrun was also investigated by Anastasopoulos et al. (2010b, 2011, 2014), using data for different activity types and multiple PPP types. These studies identified the project duration as a major influential factor for the cost overrun or cost savings. Cost overrun was also examined with respect to the successive phases of the project development, with the stage between the decision for the project implementation and the beginning of the construction works being critical for the cost overrun (Cantarelli et al., 2012).

Time delay is another factor that results in project discrepancies, especially in long-term transportation projects. For example, Bordat et al. (2004) found that approximately 12% of the contracts let by the Indiana Department of Transportation between 1996 and 2001, had an approximate delay of 115 days. Majid and McCaffer (1998) considered several groups of factors related to project planning and development (e.g., labor, equipment, material, control, etc.) and identified and ranked 25 main causes that can result in non-excusable delays. A number of studies (Ellis and Thomas, 2003; Fimpong et al., 2003; Assaf and Al-Hejji, 2006; Ambituuni, 2011; Irfan et al., 2011) identified several factors as significant causes of time delays in highway construction projects, such as design errors, impact of weather, unpredicted site conditions, modifications in the design and the scope of the project, inefficient planning and scheduling procedures, poor technical performance, and deadline contract type, to name a few.

Finally, change orders in transportation projects pertain to modifications in the project’s scope, in terms of additional requirements, amount, time, and design method alterations. Several linear regression, discrete outcome, and count data modeling techniques have been used to identify possible influential factors that can affect change orders, such as the construction complexity of the project, site conditions, the project’s final cost, the difference between the initial cost estimation (by the agency) and the winning bid amount, design deficiencies, and weather conditions (Rowland, 1981; Hester et al., 1991; Jacoby, 2001; Anastasopoulos et al., 2010c; Serag et al., 2010).

Two approaches are considered for the investigation of project discrepancies for roadway construction and preservation by PPP type. To explore the factors that affect the extent of project discrepancies for each PPP type, linear regression models are estimated for the percentage of cost savings and cost overrun, count data (Poisson) models are estimated for the change orders frequency, and hazard-based duration models are estimated for the time delay. At the pre-planning phase, many transportation agencies are as well interested in identifying factors affecting the likelihood that a project will incur project discrepancies (Gkritza and Labi, 2008; Anastasopoulos et al., 2010a, 2014). To that end, the likelihood of cost savings, cost overrun, change orders, and time delay occurrence is investigated, through the use of binary logit and probit models. Next, an overview of the methodological approaches is presented.

The percentage of cost savings, %CS_ki, and cost overrun, %CO_ki, for a project i performed under contract type k, are, respectively, calculated as follows: (1)%CSki=100×[(CBki−CAki)/​CBki], and (2)%COki=100×[(CFki−CWBki)/​CWBki], where CB_ki is the final contract cost performed under traditional contracting (which is typically based on the amount of work being measured and paid for on agreed rates for various work items), CA_ki is the final contract cost of the project (including the same work items and project characteristics) performed under the PPP approach, C_WBki is the winning bid cost of the project, and C_Fki is the final project cost upon its completion and delivery to the agency. For the two dependent variables, %CS_ki and %CO_ki, the linear regression model can be specified as: (3)%CSki=βCSki+βCSXCSki+εCSki, and (4)%COki=βCOki+βCOXCOki+εCOki, where β_CSki and β_COki are constant terms, β_CO and β_CS are vectors of estimable parameters, X_CSki and X_COki are vectors of explanatory parameters, ε_CSki and ε_COki, are the disturbance terms, and all other terms as previously defined. With regard to the estimation of the vectors of parameters, the most common approach for the regression context is the ordinary least squares estimation (for an example, see Anastasopoulos et al., 2015). However, in order to account for unobserved heterogeneity across the observations, random parameters are introduced in model estimation, thus the maximum likelihood estimation method is adopted herein. Specifically, the log-likelihood functions, for the two dependent variables, are specified as (Washington et al., 2011): (5)LL=−I2ln(2π)−I2ln(σ2)−12σ2(%CSki−XCSkiβCS)Τ(%CSki−XCSkiβCS) (6)LL=−I2ln(2π)−I2ln(σ2)−12σ2(%COki−XCOkiβCO)Τ(%COki−XCOkiβCO) where I is the number of observations, σ² is the variance of the normally distributed error terms, and all other terms are as previously defined. The maximization of the log-likelihood function yields the best specified parameter estimates of the linear regression model.

Given that a project time delay has occurred, the length of the delay can be statistically modeled as duration data using hazard-based duration modeling methods. To model the conditional probability of a project delay terminating at time t (under the condition that it has not terminated until then), a hazard function that accounts for the effect of explanatory variables is specified as (Washington et al., 2011): (7)h(t|X)=h0(t)exp(−βX), where h₀(t) is the baseline hazard (denoting the hazard when all elements of the explanatory variables vector are zero), and all other terms as previously defined. The underlying hazard function in Eq. 5 can take various parametric forms, such as Exponential, Weibull, and Log-logistic (Anastasopoulos et al., 2012, 2017). For model estimation, all three parametric forms were explored, and the Weibull model provided the best statistical fit (in terms of goodness-of-fit measures, such as log-likelihood function at convergence, McFadden pseudo-R², and Akaike Information criteria). For the Weibull model, with parameters λ > 0 and P > 0, the density function is (Washington et al., 2011): (8)f(t)=λP(λt)P−1exp[−(λt)P] and the baseline hazard in Eq. 5 becomes: (9)h(t)=λP(λt)P−1.

The Weibull model yields monotonically increasing or decreasing (over time) hazard functions, on the basis of the estimable Weibull parameter P. If P is greater than one, the hazard monotonically increases with the delay duration, indicating that the probability of a project delay terminating at time t increases over time; the opposite is observed, if P is less than one, since the hazard function monotonically decreases with the delay duration, indicating that the probability of a project delay terminating at time t decreases over time. For the estimation of the vector of parameters β, a maximum likelihood estimation method is adopted.

The frequency of change orders can be modeled using count data modeling approaches, such as the Poisson and negative binomial models, and their zero-inflated counterparts (Anastasopoulos et al., 2010c). For model estimation, all count data modeling techniques were explored, and the Poisson model gave the best overall statistical fit (in terms of goodness-of-fit measures, such as log-likelihood function at convergence, ρ², Vuong statistic, and Akaike Information criteria). For the Poisson model, the probability, P(n_i), of contract, i, to incur n change orders is (Washington et al., 2011): (10)P(ni)=exp(−λi)λinini!, where λ_i = exp(βX_i) is the expected number of change orders, and all other terms as previously defined. For model estimation, a maximum likelihood estimation method was employed, with the corresponding log-likelihood function being defined as: (11)LL(β)=Σi=1I[−exp(βΧi)+yiβΧi−LN(yi!)] where y_i is the frequency of change orders with expected value E(y_i) = λ_i, and all other terms as previously defined. Since there is not dispersion in the data, the maximum likelihood estimates of the Poisson model yield unbiased and consistent parameters.

For the likelihood of cost savings, cost overrun, change orders, and time delay occurrence, binary (since only two outcomes are considered: discrepancy and non-discrepancy occurrence) logit and probit models can be used (Washington et al., 2011). The fundamental difference between the two logit and probit approaches arises from the assumed distribution of the error terms. For the logit specification, the disturbances are assumed to be Gumbel-extreme value Type I distributed, whereas, for the probit specification, the disturbances are assumed to be normally distributed. The binary logit outcome probabilities are thus defined as (Washington et al., 2011): (12)Pki(D)=11+exp[−(βDXDki)], and the binary probit outcome probabilities as: (13)Pki(D)=Φ[βDXDki−βNDXNDkiσ], where P_ki(D) is the probability of observation, i, in PPP approach, k, incurring a discrepancy, D, or no discrepancy, ND, in terms of cost savings, cost overrun, time delay, or change orders, Φ(.) is the standardized cumulative normal distribution, and σ is a scaling parameter (which is typically set to one) that determines the discrete outcomes. For the estimation of the parameter vectors β_D and β_ND, standard maximum likelihood estimation methods are used (Washington et al., 2011). Specifically, for the probit model specification, the log-likelihood function is: (14)LL=∑i=1I[βDXDki−LNΣ∀Jexp(βJDXJDi)]; whereas, for the logit model specification, the log-likelihood function is defined as: (15)LL=Σi=1N(δDiLNΦ(βDXDki−βNDXNDkiσ)+(1−δDi)LNΦ(βDXDki−βNDXNDkiσ)) where δ_Di is equal to 1 if the observation i incurs a discrepancy, D, or zero otherwise, N denotes the number of observations, and the other terms are as previously defined.

To account for unobserved heterogeneity—a common misspecification issue—the effect of the parameters of the aforementioned modeling schemes is allowed to vary across the observations, through the use of random parameters modeling. This is an important consideration, as if unobserved heterogeneity is not addressed, the parameter estimates can be erroneous, the inferences inconsistent, and the forecasts inaccurate (Washington et al., 2011; Russo et al., 2014; Anastasopoulos, 2016; Anastasopoulos and Mannering, 2016; Mannering et al., 2016; Sarwar et al., 2016, 2017). In random parameters modeling, the coefficients become: (16)βn=β+ωn, where β_n is a vector of estimable parameters, and ω_n is a randomly distributed term (for example, a normally distributed term with mean zero and variance σ²). Under this consideration, β_n is a vector of individual parameters across observations, with its variation to be described by a density function—also referred as mixing distribution—q(β|ω), where ω refers to a vector of parameters of the density distribution (Greene, 2007; Washington et al., 2011; Anastasopoulos et al., 2012). To address the added complexity by the inclusion of random parameters in the computation of outcome probabilities, a simulation-based maximum likelihood estimation approach is employed. Specifically, various values of βs are drawn from the density function q(β|ω) and are used for the computation of the logit (or probit) outcome probabilities, as shown in Eqs 12 and 13. Numerous iterations of the same procedure provide the corresponding simulated probabilities, which are, in turn, introduced in the simulated log-likelihood function (Washington et al., 2011). As far as the sampling technique of β values from the mixing distribution is concerned, the technique of Halton draws (Halton, 1960) is employed, which can provide efficient probability approximations, by limiting the number of draws to the smallest possible extent; the non-random selection of draws provide more robust estimates, as compared to the use of purely random draws (see Bhat, 2003; Train, 2003; Washington et al., 2011, for further details on the simulation approach). For model estimation, 200 Halton draws are used, which have been shown to yield stable and accurate parameter estimates (Bhat, 2003; Milton et al., 2008; Anastasopoulos et al., 2016). For the functional form of the parameter density function, normal, Weibull, lognormal, uniform, and triangular distributions were considered in model estimation, and the normal distribution yielded the best specified model results, in terms of statistical fit. It should be noted that a parameter is considered as random when the mean and the SD of the parameter density function are statistically different from zero, at a pre-specified level of confidence (at a 0.90 level of confidence herein).

To identify the factors that affect the extent and likelihood of project discrepancies, cost- and project-specific data are used. These data have been published in previous studies (Anastasopoulos et al., 2010a, 2011; Nahidi, 2015; Nahidi et al., 2015; Sarwar and Anastasopoulos, 2016a,b) and have since been extended to include new information, in terms of the number of contracts and of the independent variables (i.e., pavement, traffic safety, and operations characteristics). Specifically, the data include information for 645 PPP contracts implemented in the USA between 1996 and 2011. In addition to traditional outsourcing contracts, six popular PPP types are represented in the data, namely, cost-plus-time (A + B), PBC, I/D, DBOM, lane rentals, and warranties. These data also include cost and time-related information (contract cost, bid cost, number of bids, cost savings, cost overrun/underrun, time delay, number of change orders and associated costs, etc.); contract duration (and extension); roadway functional classification and roadway geometrics (segment length, number of lanes, median and shoulder attributes, drainage rating, and horizontal/vertical alignment characteristics); pavement characteristics (roughness, rutting depth, and pavement condition rating); traffic characteristics (annual average daily traffic, level of service, and truck traffic); weather conditions (precipitation and temperature); and number of assets (constructed or preserved) included in the contract. In addition, these data contain information about the scope and activity type of the project (e.g., construction, repair, maintenance, and management activities), as well as the asset type (e.g., pavements, bridges, roadway cross-section elements, traffic infrastructure, landscape, and emergency facilities). Table 1 presents descriptive statistics of key variables. For a detailed description of the dataset, see Nahidi (2015) and Nahidi et al. (2015).

Tables 2–9 present the estimation results of the best model specifications (several variables and variable combinations were explored, and the ones that provided the best overall statistical fit—in terms of goodness-of-fit measures—are presented herein), along with their goodness-of-fit measures, for the extent and likelihood of project discrepancies by PPP type. The subsequent sections provide a brief discussion of the model estimation results for each discrepancy type. Note that, for brevity, key results (including only a few random parameters) are discussed in detail.

This paper seeks to provide an empirical analysis of the influence of contract, project, and roadway characteristics on common project discrepancy types (cost savings, cost overrun, change orders, and time delay), for popular roadway construction and preservation PPP contract types [traditional outsourcing, cost-plus-time (A + B), DBOM, I/D, lane rentals, PBC, and warranties]. The presented comprehensive statistical modeling framework allows the identification of factors that affect both the extent (typically used by transportation agencies in the planning phase) and the likelihood (frequently used by transportation agencies in the pre-planning phase) of project discrepancies, while accounting for unobserved factors that can vary systematically across the observations (i.e., unobserved heterogeneity). The factors that affect the extent of project discrepancies for each PPP type, are statistically modeled with random parameters linear regression models (for the cost savings and cost overrun percentages), with random parameters count data (Poisson) models (for the change orders frequency), and with random parameters hazard-based duration (Weibull) models (for the time delay duration). While random parameters (mixed) binary logit and probit models are estimated to investigate the factors affecting the likelihood of cost savings, cost overrun, change orders, and time delay occurrence.

Table 10 provides a qualitative overview of the various factors affecting the extent and the likelihood of project discrepancies, by PPP type. Although the analysis does not aim to yield explicit guidelines regarding the adoption of the most appropriate PPP type, it has the potential to provide significant insights with regard to the effectiveness of each PPP type, in the context of different project discrepancies and several contract- and project-specific characteristics. The model estimation results show that contracts with longer duration generally incur lower cost savings and have lower cost savings occurrence likelihood. Longer contract duration also results in cost overrun, time delay, and change orders increase. For most of the PPP types (A + B, DBOM, PBC, and I/D), large size projects incur a reduction in cost savings, and an increase in cost overrun and time delay; while, for DBOM, PBCs, and traditional contracts, large size projects incur an increase in change orders frequency. Furthermore, in cases of high contract cost, DBOM, I/D, and warranties are found to increase cost savings; the opposite holds for lane rentals, PBCs, and traditional contracts. The number and type of assets (constructed or preserved) included in a contract also play an important role in project discrepancies by PPP type. A general finding is that contracts with many assets incur lower cost savings, and higher cost overrun and time delay. On the other hand, the activity types have varying effects on project discrepancies for each PPP type. For example, activities such as guardrail, shoulder repair and maintenance, traffic signs and signals, and electrical and cable repair and maintenance, perform better (in terms of cost savings, cost overrun, change orders, and time delay) when they are let under lane rentals. In contrast, crack and pothole sealing, and pavement repair and maintenance, perform better (in terms of cost related discrepancies) when they are let under warranties. In addition, contracts with generally low-cost activities (such as mowing, vegetation, tree control, or landscape repair and maintenance) perform better when they are let either under lane rentals or warranties. Whereas, contracts with many and variable activities such as general management, or bridge repair and maintenance, perform better (in terms of most project discrepancies) when they are let under PBC.

In an overall assessment, large-scale roadway projects (in terms of size, duration, cost and number of assets included) may favor the adoption of PBC or I/D; on the contrary, roadways projects associated with tighter deadlines or with activities requiring high level of expertise may be better accomplished under the DBOM or the warranty contractual approaches. The latter PPP types involve significant risk transfer to the contractors, which might act as incentive toward the minimization of cost- or time-related discrepancies. However, these general findings should be carefully assessed by Public Agencies and contractors in conjunction with various location-, time-, and detailed project-specific factors, which introduce considerable heterogeneity in the decision making process.

Unlike previous studies that have investigated project discrepancies separately and—to a large extent—irrespective of the PPP type, this study provides a comprehensive framework that allows identification of various project, contract, and roadway characteristics for all project discrepancies and some of the most popular PPP types. In this context, the selection of an appropriate PPP type for a given transportation (construction or preservation) project at the planning or pre-planning phase, can be informatively supported by the attributes of the factors that are likely to affect each (separately) or all (collectively) of the project discrepancy types.

In all, this empirical study should be viewed as an incremental step toward the development of decision-making guidelines for the adoption of various PPP types, as a function of project discrepancies and several contract, project, and roadway characteristics. Extension of this work could include the collection of PPP contracts from existing regions or from regions not explored in the current study, and development of more robust statistical models with a greater number of observations. The simultaneous statistical modeling—as a system of equations—of the extent of the four different project discrepancy types could also serve as a direction for future work, as it would possibly account for common unobserved factors underlying in the error terms (in the form of cross-equation error correlation).

All authors contributed in the preparation and the completion of the submitted paper.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.