Score Matching Estimator Research Articles

Robust score matching for compositional data

The restricted polynomially-tilted pairwise interaction (RPPI) distribution gives a flexible model for compositional data. It is particularly well-suited to situations where some of the marginal distributions of the components of a composition are concentrated near zero, possibly with right skewness. This article develops a method of tractable robust estimation for the model by combining two ideas. The first idea is to use score matching estimation after an additive log-ratio transformation. The resulting estimator is automatically insensitive to zeros in the data compositions. The second idea is to incorporate suitable weights in the estimating equations. The resulting estimator is additionally resistant to outliers. These properties are confirmed in simulation studies where we further also demonstrate that our new outlier-robust estimator is efficient in high concentration settings, even in the case when there is no model contamination. An example is given using microbiome data. A user-friendly R package accompanies the article.

Venture capital investment, intellectual property rights protection and firm innovation: evidence from China

ABSTRACT We examine the heterogeneous effects of venture capital (VC) investment on firm innovation. Using a panel dataset of Chinese manufacturing firms, we find that VC-backed firms outperform non-VC-backed ones in patenting activities, new product sales, and exports because of the ex-ante selection and ex-post value-added effects of VC investment. Firms with better performance in innovation are more likely to get VC support, and such outperformance is magnified after the VC investment is made. Moreover, the impact of VC investment on firm innovation is greater when the protection of IPR is stronger. In addition, firms backed by more experienced VC firms (VCFs) generate more commercialized innovation but are less productive in patenting activities than firms backed by less experienced VCFs. Finally, firms backed by state-owned VCFs outperform in patenting activities but underperform in commercialized innovation those backed by other types of VCFs. Identification and selection issues are addressed by the propensity score matching approach and two-stage estimations.

Score Matching for Compositional Distributions

Compositional data are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. With real data, it is often the case that many of the compositional components are highly right-skewed, with large numbers of zeros. Major limitations of currently available models for compositional data include one or more of the following: insufficient flexibility in terms of distributional shape; difficulty in accommodating zeros in the data in estimation; and lack of computational viability in moderate to high dimensions. In this article, we propose a new model, the polynomially tilted pairwise interaction (PPI) model, for analysing compositional data. Maximum likelihood estimation is difficult for the PPI model. Instead, we propose novel score matching estimators, which entails extending the score matching approach to Riemannian manifolds with boundary. These new estimators are available in closed form and simulation studies show that they perform well in practice. As our main application, we analyse real microbiome count data with fixed totals using a multinomial latent variable model with a PPI model for the latent variable distribution. We prove that, under certain conditions, the new score matching estimators are consistent for the parameters in the new multinomial latent variable model.

Outcomes of non-metastatic poorly differentiated gastroenteropancreatic neuroendocrine neoplasms treated with surgery: a real-world population-based study.

To assess the outcomes of non-metastatic poorly differentiated gastroenteropancreatic neuroendocrine neoplasms (GEP-NENs) treated with radical surgery. Surveillance, Epidemiology, and End Results (SEER) database (1998-2015) was accessed, and patients with non-metastatic poorly differentiated/undifferentiated GEP-NENs were reviewed. Multivariable Cox regression analysis was used to evaluate factors affecting overall survival (OS) and cancer-specific survival (CSS). Patients treated with radical surgery were matched to those who did not undergo surgery through propensity score matching and Kaplan-Meier survival estimates were used to evaluate the impact of surgery in the post-propensity cohort. A total of 1517 patients were included. Within multivariable Cox regression models and compared to no surgery, radical surgery was associated with improved OS (HR: 0.41; 95% CI: 0.34-0.50) and CSS (HR: 0.37; 95% CI: 0.29-0.47). A total of 233 patients who underwent no surgery were then matched to 233 patients who underwent radical surgery. Within the post-propensity cohort, radical surgery was associated with improved OS (P < 0.001). Radical surgery is associated with improved survival outcomes in patients with non-metastatic poorly differentiated GEP-NENs. Further studies are required to better identify the best timing of radical surgery within the context of multimodal management.

The impact of two-child policy on household savings in China and mechanisms

ABSTRACT One-child policy has been accused of causing high saving rates in China, and this article provides direct evidences for the economic impact of the two-child policy on savings. Using China Migrants Dynamic Survey, we find the two-child policy significantly reduces the household saving rates by 1.96 percentage points in average and by 4.88 percentage points if the rural and ethnic minority groups excluded, and we also use IV and propensity score matching (PSM) estimation methods to test the robustness. Furthermore, the study shows that the two-child policy has a heterogeneous effect on the saving rates decreasing, which mainly occurs in the local hukou population group. From this perspective, the policy has a comprehensive and sustainable impact. Through mechanism analysis, we clarify that the two-child policy affects savings by increasing expenditure insignificantly; in addition to the direct effect, it mainly affects savings by transiently reducing family income. Abbreviations: IV: Instrumental variables; PSM: Propensity score matching; CPI: Consumer price index; OLS: Ordinary least squares

Fuelling financial literacy: estimating the impact of youth entrepreneurship training in Tanzania

Training programmes are popular development interventions that aim to address problems of youth unemployment. This paper estimates the impact of a youth entrepreneurship programme in Tanzania on financial literacy and employment knowledge. Using primary data within a successive cohort design in a community-led programme, the authors employed propensity score matching and fixed-effect estimation methods to assess changes in knowledge, skills and attitudes of marginalised youth. They found strong positive effects of the programme on key intermediate employment outcomes: savings ability, employment confidence and personal finance. The positive impact of this programme supports youth entrepreneurship training programme and non-experimental evaluation methods.

ECONOMIC IMPACT ASSESSMENT OF PUBLIC–PRIVATE MATCHING FUND PROGRAMS USING FIRM-LEVEL DATA

In the intermediate goods industry, largely made up of small and medium enterprises (SMEs), a government can use a matching fund to execute policies that, for example, provide funds to promote and support firms' innovative activities. This study performs an empirical analysis to investigate the additional effects when a government uses a matching fund in this way and, in particular, to analyze the growth of firms. Methodologically, to deal with the selectivity issue, we adopt a propensity score matching (PSM) estimator. We also investigate the performance of the matching fund according to changes in private shares. Our findings show that supported firms invested larger amounts in R&amp;D and procured external financing through an overall improvement in their level of reliability. However, the results also show that this was not connected to further improvements in business performance. Moreover, although our results show some positive impact on assets and R&amp;D expenditure from private investment in the matching fund, the relationship between sales and fixed assets was non-significant.

Linear estimating equations for exponential families with application to Gaussian linear concentration models

In many families of distributions, maximum likelihood estimation is intractable because the normalization constant for the density which enters into the likelihood function is not easily available. The score matching estimator [35] provides an alternative where this normalization constant is not required. For an exponential family, e.g. a Gaussian linear concentration model, the corresponding estimating equations become linear [2,36] and the score matching estimator is shown to be consistent and asymptotically normally distributed as the number of observations increase to infinity, although not necessarily efficient. For linear concentration models that are also linear in the covariance [37] we show that the score matching estimator is identical to the maximum likelihood estimator, hence in such cases it is also efficient. Gaussian graphical models and graphical models with symmetries [32] form particularly interesting subclasses of linear concentration models and we investigate the potential use of the score matching estimator for this case.

Comparative effectiveness of erlotinib versus no treatment for advanced non-small cell lung cancer patients in the Veterans Administration.

6105 Background: Erlotinib (E) is FDA-approved for second-line treatment of unselected advanced non-small cell lung cancer (aNSCLC) patients. Clinical trials have shown increased response rates with E in aNSCLC patients having East Asian ethnicity, female gender, never-smoking history, or adenocarcinoma histology. The objective of this study was to compare the real-world effectiveness of E versus no treatment (NT) for first- and second-line treatment of aNSCLC patients in the Veterans Administration (VA). Methods: All incident aNSCLC cases diagnosed in the VA during 2007 were identified through the VA Central Cancer Registry, a subset of which underwent medical record abstraction through the VA External Peer Review Program. Abstracted records were then merged with national VA Decision Support System pharmacy and Corporate Data Warehouse encounters data through 2010. Treatment lines were determined through adaptation of a published algorithm. The impact of E versus NT on overall survival for each treatment line was then evaluated using 1:N greedy propensity score matching (PSM) and 2-stage residual inclusion (2SRI) estimation. Results: Among 1965 aNSCLC patients assessed for first-line treatment, 78 (4%) received E and 782 (40%) received NT; among 1124 assessed for second-line treatment, 128 received E (7%) and 638 (33%) received NT. 1:3 PSM of E cases to NT controls showed no difference in overall survival by Kaplan-Meier estimation in the first- (median 2.6 vs. 2.9 mos., p-value=0.86) and second-line (3.4 vs. 3.2 mos., p=0.85) settings. Chemotherapy use by Veterans Integrated Service Network was selected as the instrumental variable for 2SRI. Expected mean survival of E versus NT was similarly not statistically prolonged in the first- (E:NT survival time ratio 2.55, p=0.35) and second-line (2.49, p=0.32) settings. Conclusions: For a population with few aNSCLC patients having 3 out of the 4 clinicopathologic characteristics associated with improved response, E did not appear to confer a survival advantage over NT. Linking mutation results to observational datasets may improve comparative effectiveness research of personalized medicine in oncology.

Some extensions of score matching

Many probabilistic models are only defined up to a normalization constant. This makes maximum likelihood estimation of the model parameters very difficult. Typically, one then has to resort to Markov Chain Monte Carlo methods, or approximations of the normalization constant. Previously, a method called score matching was proposed for computationally efficient yet (locally) consistent estimation of such models. The basic form of score matching is valid, however, only for models which define a differentiable probability density function over R n . Therefore, some extensions of the framework are proposed. First, a related method for binary variables is proposed. Second, it is shown how to estimate non-normalized models defined in the non-negative real domain, i.e. R + n . As a further result, it is shown that the score matching estimator can be obtained in closed form for some exponential families.