Prevent object from jumping to center point when dragging starts

I have a script for dragging GameObjects around, but at the moment, whenever I start to drag on the object it jumps to the center the object onto the pointer. What I'd like to achieve is regardless of where I start to drag on the object it initiates drag at that point instead of jumping to the object center first. What do I need to modify in my OnDrag or OnBeginDrag method to achieve this?

 using UnityEngine;
 using UnityEngine.UI;
 using System.Collections;
 using UnityEngine.EventSystems;
 using System.Collections.Generic;
 
 public class DragHandling : MonoBehaviour, IBeginDragHandler, IDragHandler, IEndDragHandler, IPointerClickHandler
 {
     public float partScale;
 
     [HideInInspector] public Transform placeholderParent = null;
     [HideInInspector] public Transform parentToReturnTo = null;
     [HideInInspector] public GameObject trashCan; 
     [HideInInspector] public GameObject partsPanel;
     [HideInInspector] public GameObject partsWindow;
     [HideInInspector] public GameObject buildBoard;
 
     GameObject placeholder = null;
     GameObject dragLayer;
     Vector3 buildPanelScale;
     Vector3 partsPanelScale = new Vector3(1.0f, 1.0f, 1.0f);
     Vector3 startPosition;
 
     // PolygonCollider2D collider;
 
     void Start ()
     {
         dragLayer = GameObject.FindGameObjectWithTag("DragLayer");
         buildBoard = GameObject.FindGameObjectWithTag("Board");
         partsPanel = GameObject.FindGameObjectWithTag("Parts");
         partsWindow = GameObject.FindGameObjectWithTag("PartsWindow");
         trashCan = GameObject.FindGameObjectWithTag("Trash");
 
         // collider = transform.GetComponent<PolygonCollider2D>();
     }
 
     #region IPointerClickHandler implementation
 
     public void OnPointerClick (PointerEventData eventData)
     {
         if(transform.parent.gameObject == buildBoard)
             transform.SetAsLastSibling();
     }
 
     #endregion
 
     #region IBeginDragHandler implementation
 
     public void OnBeginDrag (PointerEventData eventData)
     {
         // create placeholder gap and hold correct position in layout
         placeholder = new GameObject();
         placeholder.transform.SetParent(transform.parent);
         placeholder.transform.SetSiblingIndex(transform.GetSiblingIndex());
         parentToReturnTo = transform.parent;                                    // store original parent location
         placeholderParent = parentToReturnTo;                                    // set placeholder gameobject transform
         startPosition = transform.position;
         GetComponent<CanvasGroup>().blocksRaycasts = false;                        // turn off image raycasting when dragging image in order to see what's behind the image            
     }
 
     #endregion
 
     #region IDragHandler implementation
     
     public void OnDrag (PointerEventData eventData)
     {
         Vector3 mousePosition = new Vector3(eventData.position.x, eventData.position.y, 0);
         transform.position = Input.mousePosition;                                            // set object coordinates to mouse coordinates
 
         if(transform.parent.gameObject == partsPanel)
             transform.SetParent(dragLayer.transform);                                        // pop object to draglayer to move object out of parts Panel
         if(transform.parent.gameObject == buildBoard)
             transform.SetParent(dragLayer.transform);
     }
     
     #endregion
 
     #region IEndDragHandler implementation
 
     public void OnEndDrag (PointerEventData eventData)
     {
         transform.SetParent(parentToReturnTo);                                    // Snaps object back to orginal parent if dropped outside of a dropzone
         transform.SetSiblingIndex(placeholder.transform.GetSiblingIndex());        // Returns card back to placeholder location
         GetComponent<CanvasGroup>().blocksRaycasts = true;                        // turn Raycast back on
         Destroy(placeholder);                                                    // kill the placeholder if object hits a drop zone or returns to parts panel
 
         if(transform.parent.gameObject == buildBoard)
         {
             buildPanelScale = new Vector3(partScale, partScale, partScale);
             transform.localScale = buildPanelScale;
             transform.SetAsLastSibling();                                        // always place last piece on top
         }
         if(transform.parent.gameObject == partsPanel)
             transform.localScale = partsPanelScale;
     }
 
     #endregion
 
 }